Deck 24: Linear Programming

Question 1

16)ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Determine the objective function for the LP formulation.

A)Maximize profit = $11 * (Number of shirts to be produced + Number of pairs of pants to be produced)
B)Maximize profit = $5 * Number of shirts to be produced
C)Maximize profit = $6 * Number of pairs of pants to be produced
D)Maximize profit = ($5 * Number of shirts to be produced)+ ($6 * Number of pairs of pants to be produced)

Answer 1

D

Question 2

17)ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Determine the nonnegative constraint for the LP formulation.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.

A)X₁ and X₂ > 0
B)X₁ and X₂ ≥ 0
C)X₁ and X₂ ≤ 0
D)X₁ and X₂ = 0

Answer 2

B

Question 3

7)All linear programming problems must have ______ distinct features.

A)three
B)four
C)five
D)six

Answer 3

B

Question 4

2)Which of the following is a mathematical modeling technique that managers can use in making decisions that involve optimizing an objective,subject to constraints?

A)optimization
B)estimation
C)linear programming
D)transportation model

Question 5

6)Determining the supply of resources needed to meet demand for the intermediate time frame at the minimum cost is an example of applying linear programming to solving ______ problems.

A)financial planning
B)production planning
C)assignment
D)transportation

Question 6

15)ABC,Inc.,is a small clothing manufacturer that produces polo shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hours cutting machine time.Production of one polo shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each polo shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.How many decision variables are there in this LP formulation?

A)one
B)two
C)three
D)four

Question 7

3)In linear programming,advertising dollars budgeted for a marketing campaign is an example of ______.

A)a variable
B)a resource
C)a constraint
D)an objective

Question 8

12)The requirement of linear programming is that the objective function and the constraints have ______ relationship.

A)independent
B)linear
C)exponential
D)nonlinear

Question 9

20)The graphical method is appropriate for solving simple linear programming problems involving ______ decision variables.

A)one
B)two
C)three
D)four

Question 10

18)ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Determine sewing time constraint for the LP formulation.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.

A)3X₁ + 2X₂ ≤ 240
B)X₁ + 1.5X₂ ≤ 150
C)3X₁ + 2X₂ ≤ 150
D)X₁ + 1.5X₂ ≤ 240

Question 11

1)The limited availability of resources can be referred to as ______.

A)constraints
B)variables
C)consequences
D)state of nature

Question 12

11)The resource constraints are modeled in LP mathematically as ______.

A)inequalities
B)equalities or inequalities
C)linearity
D)variables

Question 13

4)In linear programming,maximizing profits or minimizing costs is an example of ______.

A)a variable
B)a resource
C)a constraint
D)an objective

Question 14

9)Which of the following is FALSE about objective functions in linear programming (LP)?

A)Every LP problem will have an objective function.
B)An objective function can be either maximized or minimized.
C)The objective of an LP problem expressed mathematically is referred to as an objective function.
D)The objective for an LP problem should be expressed explicitly in monetary units.

Question 15

8)Which of the following is NOT one of the features of a linear programming problem?

A)decision variables
B)consequences
C)constraints
D)linearity

Question 16

10)______ in linear programming are an alternative course of action-for example,determining the number of shipping routes for transporting goods from the available alternative choices.

A)Decision variables
B)Consequences
C)Constraints
D)Linearity

Question 17

19)ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Determine cutting time constraint for the LP formulation.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.

A)3X₁ + 2X₂ ≤ 240
B)X₁ + 1.5X₂ ≤ 150
C)3X₁ + 2X₂ ≤ 150
D)X₁ + 1.5X₂ ≤ 240

Question 18

13)Using linear programming (LP)to determine the optimum investment portfolio that will achieve certain returns while minimizing investment risks is an example of applying LP to solving ______ problems.

A)financial planning
B)production planning
C)assignment
D)transportation

Question 19

5)Determining the shipment of goods from multiple sources to multiple destinations to minimize transportation costs is an example of applying linear programming to solving ______ problems.

A)financial planning
B)production planning
C)assignment
D)transportation

Question 20

14)ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hours of cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Which of the following is the decision variable for the LP formulation?

A)total revenue generated
B)number of sewing hours and number of cutting hours required
C)number of shirts and number of pairs of pants to be produced
D)total production time

Question 21

23)ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.What is the total profit at the optimal solution?

A)$250
B)$398
C)$624
D)$583

Question 22

25)ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.Which one of the following corner point (x1,x2)yields the maximum profit in this LP formulation?

A)(24,84)
B)(80,100)
C)(84,24)
D)(80,0)

Question 23

28)When the LP problem has more than two decision variables,the ______ is appropriate for searching the optimal solution.

A)graphical method
B)corner point method
C)simplex method
D)iso-profit line method

Question 24

21)Constraints in LP problems that do not affect the boundaries of the feasible solution region are referred to as ______.

A)redundant constraints
B)binding constraints
C)restrictive constraints
D)optimal constraints

Question 25

24)ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Determine cutting time constraint for the LP formulation.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.Which one of the following is NOT one of the corner points (x1,x2)in this LP formulation?

A)(24,84)
B)(80,100)
C)(0,100)
D)(80,0)

Question 26

29)______ are constraints that form the corner points at the boundaries of the feasible solution region and limit the values of the decision variables,which in turn,limit the objective function values.

A)Binding constraints
B)Nonbinding constraints
C)Redundant constraints
D)Optimal constraints

Question 27

22)According to the mathematical theory underlying LP problems,the optimal solution to an LP problem will occur at ______.

A)one of the corner points of the feasible space
B)all of the corner points of the feasible space
C)any point inside the feasible space
D)any point outside the feasible space

Question 28

35)For binding constraints at optimality,the right-hand value should be ______ the left-hand value.

A)greater than
B)less than
C)equal to
D)in proportion to

Question 29

26)ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.Determine the value of X₁ and X₂ (that maximizes profit)using corner point method.

A)X₁ = 0,X₂ = 100
B)X₁ = 120,X₂ = 0
C)X₁ = 84,X₂ = 24
D)X₁ = 24,X₂ = 84

Question 30

31)Which of the following is a method in which parallel cost lines are plotted in the LP graphical solution approach to determine the least cost solution to LP problems with cost minimization objective?

A)graphical method
B)corner point solution method
C)iso-cost line method
D)iso-profit line method

Question 31

38)Which of the following is an algorithm that provides a systematic way of examining the corner or extreme points of the feasible region of more complex LP problems to determine the optimal value of the objective function?

A)graphical method
B)corner point method
C)simplex method
D)iso-profit line method

Question 32

39)In the Excel Solver parameters window,the cell reference for the objective function is an input into which of the following fields?

A)Set Objective
B)By Changing Variable Cells
C)Subject to Constraints
D)Select a Solving Method

Question 33

34)______ is the range of values of the objective function within which the optimal values of the decision variables will not change.

A)Range of feasibility
B)Range of optimality
C)Range of redundancy
D)Range of continuity

Question 34

36)At optimality,if the left-hand side values are greater than the right-hand side values,we have ______.

A)slack
B)profit
C)loss
D)surplus

Question 35

40)In the Excel Solver parameters window,which of the following options should be selected from the "Select a Solving Method" drop-down menu to solve an LP problem?

A)GRG Onlinear
B)Simplex LP
C)Evolutionary
D)Complex LP

Question 36

32)Which of the following is a method in which parallel profit lines are plotted in the LP graphical solution approach to determine the maximum profit solution to LP problems with profit maximization objective?

A)graphical method
B)corner point solution method
C)iso-cost line method
D)iso-profit line method

Question 37

37)At optimality,if the left-hand side values are lesser than the right-hand side values,we have ______.

A)slack
B)profit
C)loss
D)surplus

Question 38

30)The ______ is a process in which each of the corner points occurring at the boundaries of the feasible solution space is examined to determine the optimal solution.

A)graphical method
B)corner point solution method
C)iso-cost line method
D)iso-profit line method

Question 39

27)Which of the following methods do we use in conjunction with the corner point method to determine the maximum profit solution to LP problems with profit maximization objective?

A)iso-cost line method
B)sensitivity analysis method
C)simplex method
D)iso-profit line method

Question 40

33)Under instances where the iso-profit line is parallel to one of the constraints that define the boundaries of the feasible solution region,every combination of values of the decision variables that fall on that segment of the constraint line that just touches the feasible solution region is referred to as ______.

A)multiple optimum solutions
B)local optimum solutions
C)global optimum solution
D)single optimum solutions

Question 41

46)A sensitivity analysis report generated by Excel Solver includes the ______ and the ______.

A)fixed cells table,variable cells table
B)constraint table,variable cells table
C)constraint table,objective table
D)variable cells table,decision variables table

Question 42

60)XYZ manufactures four types of plywood panels.Each product must go through the following operations: patching,grading,gluing,and baking.The time requirements for each panel,the capacity available,the minimum production requirements,and the profit contributions per panel are tabled here.Which of the following represents the production constraint for the aircraft plywood panel? Let x1 = Number of soft panels to be made,x2 = Number of hardwood panels to be made,x3 = Number of tropical panel to be made,and x4 = Number of aircraft panels to be made.

A)X₁ ≥ 100
B)0.5X₁ + 1X₂ + 2.0X₃ + 1.5X₄ ≤ 2,000
C)X₄ ≥ 300
D)X₁ + 2X₂ + 3X₃ + 4X₄ ≤ 4,000

Question 43

45)The sensitivity analysis report generated by Excel solver has ______ major components.

A)two
B)three
C)four
D)five

Question 44

59)XYZ manufactures four types of plywood panels.Each product must go through the following operations: patching,grading,gluing,and baking.The time requirements for each panel,the capacity available,the minimum production requirements,and the profit contributions per panel are tabled here.Determine the capacity constraint for patching operation.Let x1 = Number of soft panels to be made,x2 = Number of hardwood panels to be made,x3 = Number of tropical panel to be made,and x4 = Number of aircraft panels to be made.

A)X₁ ≥ 100
B)0.6X₁ + 1X₂ + 2.0X₃ + 2.5X₄ ≤ 2,500
C)X₄ ≥ 250
D)X₁ + 2X₂ + 3X₃ + 4X₄ ≤ 4,000

Question 45

47)Consider the portion of the sensitivity analysis report that follows.The current optimal solution will not change as long as the objective coefficient of X₁ is within the range of ______.

A)4 to 9
B)1 to 4
C)5 to 9
D)3 to 6

Question 46

53)Consider the portion of the sensitivity analysis report that follows.Increasing the right-hand side constraint by 1 unit for $I$8 (150 to 151)will result in which of the following?

A)decrease the profit by $0.6
B)increase the profit by $3.2
C)increase the profit by $0.6
D)decrease the profit by $3.2

Question 47

58)XYZ manufactures four types of plywood panels.Each product must go through the following operations: patching,grading,gluing,and baking.The time requirements for each panel,the capacity available,the minimum production requirements,and the profit contributions per panel are tabled here.Identify the objective function.Let x1 = Number of soft panels to be made,x2 = Number of hardwood panels to be made,x3 = Number of tropical panel to be made,and x4 = Number of aircraft panels to be made.

A)Maximize profits = 8X₁ + 12X₂ + 18X₃ + 30X₄
B)Maximize profits = 7X₁ + 10X₂ + 15X₃ + 20X₄
C)Minimize costs = 8X₁ + 12X₂ + 18X₃ + 30X₄
D)Minimize costs = 7X1 + 10X2 + 15X3 + 20X4

Question 48

49)Changing the value of the objective coefficient will change ______.

A)final value
B)optimal solution
C)total profits
D)constraints

Question 49

51)__________ is the price one would will be willing to pay for acquiring an additional unit of a resource.

A)Final cost
B)Reduced cost
C)Shadow price
D)Single price

Question 50

44)Once the Solver tool is activated,it will appear under the ______ tab in the tool bar.

A)Formulas
B)Data
C)Developer
D)View

Question 51

55)Consider the sensitivity analysis report that follows.The shadow price of $0.6 is valid as long as the right-hand constraint of 240 is within the range of ______.

A)200 to 450
B)150 to 240
C)200 to 300
D)40 to 210

Question 52

43)In the Excel Solver parameters window,which of the following buttons should be clicked to add a constraint?

A)Add
B)Change
C)Reset
D)Load/Save

Question 53

48)The ______column(s)in the sensitivity analysis report show(s)the extent to which the profit per unit of the decision variables can be changed without affecting the current optimal solution.

A)final value
B)reduced cost
C)shadow price
D)allowable increase and allowable decrease

Question 54

50)The price associated with a resource that indicates how much more profit would be earned by increasing the amount of the resource by one unit is called ______.

A)final cost
B)reduced cost
C)shadow price
D)single price

Question 55

42)A(n)______ helps in the determination of how sensitive the current optimal solution is to changes in the input parameter values.

A)feasibility report
B)answer report
C)sensitivity analysis report
D)error report

Question 56

54)Consider the portion of the sensitivity analysis report that follows.Decreasing the right-hand side constraint by 1 unit for $I$8 (from 150 to 149)will result in which of the following?

A)decrease the profit by $0.6
B)increase the profit by $3.2
C)increase the profit by $0.6
D)decrease the profit by $3.2

Question 57

41)In the Excel Solver parameters window,the cell references for the decision variables are to be inputted into which field?

A)Set Objective
B)By Changing Variable Cells
C)Subject to Constraints
D)Select a Solving Method

Question 58

56)Consider the portion of the sensitivity analysis report that follows.The shadow price of $3.2 is valid as long as the right-hand constraint of 150 is within the range of ______.

A)30 to 70
B)30 to 150
C)150 to 220
D)80 to 180

Question 59

57)XYZ manufactures four types of plywood panels.Each product must go through the following operations: patching,grading,gluing,and baking.The time requirements for each panel,the capacity available,the minimum production requirements,and the profit contributions per panel are tabled here.How many decision variables does this LP problem have?

A)two
B)three
C)four
D)eight

Question 60

52)Consider the portion of the sensitivity analysis report that follows.Increasing the right-hand side constraint for $I$7 by 1 unit (240 to 241)will result in which of the following?

A)decrease the profit by $0.6
B)increase the profit by $3.2
C)increase the profit by $0.6
D)decrease the profit by $0.6

Question 61

79)Diamond Plywood,Inc.,manufactures four types of plywood panels.Each product must go through the following operations: patching,grading,gluing,and baking.The time in hours required for each operation for each panel,the total capacity available for each these operations in a given month,as well as the minimum production requirements and the profit contributions per panel are given in the following table.Based on this information,what is the maximum profit that Diamond Plywood can generate?

A)$21,800
B)$34,600
C)$18,900
D)$26,400

Question 62

70)In order to fertilize his vegetable farm,John,a farmer,needs to choose from two fertilizers: Nitro Plus and Phosphate Max.Each bag of Nitro Plus costs $7 and contains 8 pounds of nitrogen and 6 pounds of phosphate.Each bag of Phosphate Max costs $9 and contains 4 pounds of nitrogen and 8 pounds of phosphate.John's vegetable farm requires at least 32 pounds of nitrogen and 48 pounds of phosphate.(Assume fractions of a bag are allowed).At the optimal solution,the total fertilizer costs are ______.

A)$29.80
B)$54.40
C)$76.25
D)$80.00

Question 63

74)In order to fertilize his vegetable farm,John,a farmer,needs to choose from two fertilizers: Nitro Plus and Phosphate Max.Each bag of Nitro Plus costs $7 and contains 8 pounds of nitrogen and 6 pounds of phosphate.Each bag of Phosphate Max costs $9 and contains 4 pounds of nitrogen and 8 pounds of phosphate.John's vegetable farm requires at least 32 pounds of nitrogen and 48 pounds of phosphate.(Assume fractions of a bag are allowed).At the optimal solution,what is the cost of Phosphate Max used by John?

A)$32.85
B)$43.20
C)$37.65
D)$26.45

Question 64

76)In order to fertilize his vegetable farm,John,a farmer,needs to choose from two fertilizers: Nitro Plus and Phosphate Max.Each bag of Nitro Plus costs $7 and contains 8 pounds of nitrogen and 6 pounds of phosphate.Each bag of Phosphate Max costs $9 and contains 4 pounds of nitrogen and 8 pounds of phosphate.John's vegetable farm requires at least 32 pounds of nitrogen and 48 pounds of phosphate.(Assume fractions of a bag are allowed).At the optimal solution,what is the amount of phosphate from the Nitro Plus brand?

A)9.60
B)12.35
C)17.65
D)11.55

Question 65

75)In order to fertilize his vegetable farm,John,a farmer,needs to choose from two fertilizers: Nitro Plus and Phosphate Max.Each bag of Nitro Plus costs $7 and contains 8 pounds of nitrogen and 6 pounds of phosphate.Each bag of Phosphate Max costs $9 and contains 4 pounds of nitrogen and 8 pounds of phosphate.John's vegetable farm requires at least 32 pounds of nitrogen and 48 pounds of phosphate.(Assume fractions of a bag are allowed).At the optimal solution,what is the amount of phosphate from the Phosphate Max brand?

A)23.20
B)38.40
C)17.65
D)15.80

Question 66

71)In order to fertilize his vegetable farm,John,a farmer,needs to choose from two fertilizers: Nitro Plus and Phosphate Max.Each bag of Nitro Plus costs $7 and contains 8 pounds of nitrogen and 6 pounds of phosphate.Each bag of Phosphate Max costs $9 and contains 4 pounds of nitrogen and 8 pounds of phosphate.John's vegetable farm requires at least 32 pounds of nitrogen and 48 pounds of phosphate.(Assume fractions of a bag are allowed).At the optimal solution,how many bags of Phosphate Max does John use?

A)3.2 bags
B)1.6 bags
C)2.1 bags
D)4.8 bags

Question 67

66)Which of the following is NOT a feature common to all linear programming problems?

A)objective function
B)decision variable
C)profitability
D)constraints

Question 68

62)A school is trying to determine a nutritional diet to feed its students.The objective is to minimize cost,subject to meeting the minimum nutritional requirements of protein,calcium,and calories.The cost and nutritional content of each food,along with the minimum nutritional requirements,are shown here.Let K and T be the number pounds of kidney beans and tofu to be purchased.Which of the following is the constraint on the units of calories?

A)15K + 5T ≥ 30
B)10K + 10T ≥ 40
C)3K + 9T ≥ 18
D)K,T ≥ 0

Question 69

72)In order to fertilize his vegetable farm,John,a farmer,needs to choose from two fertilizers: Nitro Plus and Phosphate Max.Each bag of Nitro Plus costs $7 and contains 8 pounds of nitrogen and 6 pounds of phosphate.Each bag of Phosphate Max costs $9 and contains 4 pounds of nitrogen and 8 pounds of phosphate.John's vegetable farm requires at least 32 pounds of nitrogen and 48 pounds of phosphate.(Assume fractions of a bag are allowed).At the optimal solution,how many bags of Nitro Plus does John use?

A)3.2 bags
B)1.6 bags
C)2.1 bags
D)4.8 bags

Question 70

78)In order to fertilize his vegetable farm,John,a farmer,needs to choose from two fertilizers: Nitro Plus and Phosphate Max.Each bag of Nitro Plus costs $7 and contains 8 pounds of nitrogen and 6 pounds of phosphate.Each bag of Phosphate Max costs $9 and contains 4 pounds of nitrogen and 8 pounds of phosphate.John's vegetable farm requires at least 32 pounds of nitrogen and 48 pounds of phosphate.(Assume fractions of a bag are allowed).At the optimal solution,what is the amount of nitrogen from the Phosphate Max brand?

A)11.45
B)19.20
C)17.65
D)11.55

Question 71

77)In order to fertilize his vegetable farm,John,a farmer,needs to choose from two fertilizers: Nitro Plus and Phosphate Max.Each bag of Nitro Plus costs $7 and contains 8 pounds of nitrogen and 6 pounds of phosphate.Each bag of Phosphate Max costs $9 and contains 4 pounds of nitrogen and 8 pounds of phosphate.John's vegetable farm requires at least 32 pounds of nitrogen and 48 pounds of phosphate.(Assume fractions of a bag are allowed).At the optimal solution,what is the amount of nitrogen from the Nitro Plus brand?

A)11.45
B)12.80
C)17.65
D)11.55

Question 72

80)Diamond Plywood,Inc.,manufactures four types of plywood panels.Each product must go through the following operations: patching,grading,gluing,and baking.The time in hours required for each operation for each panel,the total capacity available for each these operations in a given month,as well as the minimum production requirements and the profit contributions per panel are given in the following table.Based on this information,at the optimal production point what is the quantity of soft plywood panels that Diamond Plywood will produce?

A)1,050
B)840
C)925
D)780

Question 73

68)Enrobe Textiles,Inc.,is a small clothing manufacturer that produces men's polo shirts and pants.The production manager,Zhang Wei,uses two primary resources: sewing machine hours and cutting machine hours.For next month's production of shirts and pants,Mr.Wei can schedule up to 300 hours of sewing machine time and up to 240 hours of cutting machine time.Production of each polo shirt requires 3.0 hours of sewing time and 1.0 hour of cutting time.Each pair of pants requires 2.0 hours of sewing time and 2.0 hours of cutting time.Based on the analysis of cost and sales figures,Mr.Wei estimates that each polo shirt will yield a profit of $5,and each pair of pants will generate a profit of $7.Given this scenario,what will be the maximum profits that Enrobe Textiles can achieve?

A)$525
B)$390
C)$450
D)$885

Question 74

73)In order to fertilize his vegetable farm,John,a farmer,needs to choose from two fertilizers: Nitro Plus and Phosphate Max.Each bag of Nitro Plus costs $7 and contains 8 pounds of nitrogen and 6 pounds of phosphate.Each bag of Phosphate Max costs $9 and contains 4 pounds of nitrogen and 8 pounds of phosphate.John's vegetable farm requires at least 32 pounds of nitrogen and 48 pounds of phosphate.(Assume fractions of a bag are allowed).At the optimal solution,what is the cost of Nitro Plus used by John?

A)$12.85
B)$11.20
C)$7.65
D)$16.45

Question 75

63)A school is trying to determine a nutritional diet to feed its students.The objective is to minimize cost,subject to meeting the minimum nutritional requirements of protein,calcium,and calories.The cost and nutritional content of each food,along with the minimum nutritional requirements,are shown here.Let K and T be the number pounds of kidney beans and tofu to be purchased.Which of the following is the optimal solution values of the decision variables?

A)K=1,T =3
B)K=3,T =1
C)K=2,T=2
D)K=4,T=1

Question 76

67)In an LP problem,changes in resource availability will result in a change of ______.

A)the objective function
B)the decision variables
C)the feasible solution region
D)the optimal solution

Question 77

61)A school is trying to determine a nutritional diet to feed its students.The objective is to minimize cost,subject to meeting the minimum nutritional requirements of protein,calcium,and calories.The cost and nutritional content of each food,along with the minimum nutritional requirements,are shown here.Let K and T be the number pounds of kidney beans and tofu to be purchased.Determine the objective function.

A)Minimize cost = $0.90K + $1.50T
B)Minimize cost = 1K + 1T
C)Maximize cost = $0.90K + $1.50T
D)Maximize cost = $1.00K + $1.50T

Question 78

65)Consider the portion of the sensitivity analysis report that follows.Decreasing the right-hand constraint Calcium by 1 unit (30 to 29)will result in which of the following?

A)decrease cost by $0.225
B)does not affect cost
C)increase cost by $0.225
D)increase cost by $0.025

Question 79

64)Consider the portion of the sensitivity analysis report that follows.The allowable range of optimality for variable Kidney Beans is from ______ to ______.

A)0.9 to 1.5
B)0.1 to 0.5
C)0.5 to 0.167
D)20 to 40

Question 80

69)Enrobe Textiles,Inc.,is a small clothing manufacturer that produces men's polo shirts and pants.The production manager,Zhang Wei,uses two primary resources: sewing machine hours and cutting machine hours.For next month's production of shirts and pants,Mr.Wei can schedule up to 300 hours of sewing machine time and up to 240 hours of cutting machine time.Production of each polo shirt requires 3.0 hours of sewing time and 1.0 hour of cutting time.Each pair of pants requires 2.0 hours of sewing time and 2.0 hours of cutting time.Based on the analysis of cost and sales figures,Mr.Wei estimates that each polo shirt will yield a profit of $5,and each pair of pants will generate a profit of $7.Given this scenario,what will be the combination of shirts and pants that will yield maximum profits?

A)30 pants and 105 shirts
B)210 pants and 45 shirts
C)80 pants and 55 shirts
D)120 pants and 185 shirts