Question 1

Most of the large-scale linear programming problems are solved using:

Accepted Answer

A) the graphical approach. 
B) spreadsheet-based linear programming computer programs packages. 
C) standard differential calculus techniques. 
D) a combination of algebraic and geometric techniques. 
E) the matrix algebra.

Question 2

A small machine shop produces steel shafts and metal plates.The production process depends on labor,milling machine hours,and lathe machine hours.The firm tries to identify how many metal shafts and plates should be produced per week in order to maximize profit.Which,among the following,are the decision variables?

Accepted Answer

A) Profit contributions of shafts and plates 
B) Maximum weekly labor hours available 
C) Milling and lathe machine hours available per week 
D) Quantities of shafts and plates produced per week 
E) The total profit earned by the shop

Question 3

In a linear programming problem,there are 3 binding constraints.Constraint A has slope -1.5,constraint B has slope -0.5,and constraint C has slope -0.2.The objective function's slope is -1.2.Where would the optimal solution lie?

Accepted Answer

A) At the intersection of constraints A and B 
B) At the intersection of constraints B and C 
C) At the intersection of constraint A and the horizontal axis 
D) At the intersection of constraint C and the vertical axis 
E) Anywhere along constraint A

Question 4

A shadow price measures:

Accepted Answer

A) the impact of all nonbinding constraints on the objective function simultaneously. 
B) the market price of the resource in question. 
C) the revenue earnings from the possible sale of goods. 
D) the change in the value of the objective function associated with a unit change in the resource.. 
E) the amount of loss incurred by not operating at the optimal point of the feasible region.

Question 5

A manufacturer of leather goods produces two models of briefcases-the Executive (E)and the Student (S).Each unit of the E requires 1 square yard of leather,2.5 hours of labor,and 1 hour of machine time.The S requires 0.75 square yard of leather,2 hours of labor,and 0.5 hours of machine time.Each unit of E contributes $8 of profit while S contributes $5.The manufacturer has 500 square yards of leather available per week,400 labor hours,and 180 machine hours.Formulate as a linear programming problem.The basic objective is to maximize profit.

Accepted Answer

The answer of A manufacturer of leather goods produces two...

Question 6

A firm is pondering over the introduction of a new good with a profit contribution of $70 per unit.Each unit of the good uses 2 units of input A and 3 units of input B.The shadow price of A is $10,and the shadow price of input B is $15.Which of the following statements is true?

Accepted Answer

A) The firm should produce the new good. 
B) The opportunity cost of producing the new good is $75. 
C) The firm should not produce the new good. 
D) Producing the new good will earn a profit of $10. 
E) Producing the new good will earn a loss of $5.

Question 7

A firm is maximizing profit by producing goods X and Y,using resources A and B.The firm is fully utilizing its supply of resource A,while a surplus of resource B is available.The profit contributions from per units of goods X and Y are $5 and $4 respectively.The firm is considering expansion of its supply of resource A (at a cost of $8 per unit).Increasing A by one unit would allow the firm to produce 3 additional units of X,while producing 1 fewer units of Y.Should the firm expand its supply of A? Explain.

Accepted Answer

The answer of A firm is maximizing profit by producing...

Question 8

A new product should be introduced if its profit contribution:

Accepted Answer

A) exceeds the shadow price of each resource needed to produce it. 
B) is less than the opportunity cost of producing it. 
C) exceeds the total value of the resources used,valued at their respective shadow prices. 
D) is greater than zero. 
E) is greater than the profit contributions of the other goods produced by the firm.

Question 9

A firm can profitably introduce a new activity if and only if:

Accepted Answer

A) the activity's direct benefit exceeds its opportunity cost. 
B) .the activity's direct benefit equals its opportunity cost. 
C) all the constraints become nonbinding. 
D) the slope of the resource constraint equals the slope of the objective function. 
E) the shadow price of any one of the resources becomes zero.

Question 10

A beverage producer produces cola at two bottling plants and distributes it to 4 major cities in the Southeast.The table below shows the bottling plant capacities,the number of cases to be shipped to each city,and the transport costs ($ per case)between plants and cities.The producer's objective is to meet its delivery requirements while minimizing its total transport costs.
  (a)Formulate the firm's linear programming problem.

Accepted Answer

The answer of A beverage producer produces cola at two...

Question 11

If constraints in a linear programing problem take the form 2X + Y  800 and X + 2Y  700.The optimal solution is:

Accepted Answer

A) X = 300 and Y = 200. 
B) X = 200 and Y = 300. 
C) X = 100 and Y = 300. 
D) X = 400 and Y = 0. 
E) X = 200 and Y = 400.

Question 12

Determine the feasible region given the following constraints:
4x + 3y $\le$ 120
x $\le$ 20
y $\ge$ 10
x,y $\ge$ 0

Accepted Answer

The answer of Determine the feasible region given the following...

Question 13

In a linear programming problem,the inequalities,X + 2Y ≤ 12 and 3X + 4Y  28,hold as binding constraints.The problem's optimal solution would be:

Accepted Answer

A) X = 4,and Y = -4. 
B) X = 4,and Y = 8. 
C) X = 4,and Y = 4. 
D) X = 8,and Y = 4. 
E) X = Y = 8.

Question 14

A producer of two types of fine chocolate bars utilizes four basic ingredients: milk,sugar,cocoa,and almonds.The milk bar (M)requires 8 ounces of milk,2 ounces of sugar,and 3 ounces of cocoa.The almond bar (A)requires 5 ounces of milk,1.5 ounces of sugar,2.5 ounces of cocoa,and 2 ounces of almonds.The profit contribution of each bar is $.50.The daily availability of the ingredients is limited up to 5,000 ounces of milk,1,200 ounces of sugar,2,000 ounces of cocoa,and 1,000 ounces of almonds.
(a)Formulate and solve the producer's linear programming problem.

Accepted Answer

The answer of A producer of two types of fine...

Question 15

In a linear programming problem involving two decision variables,a change in one of their coefficients will:

Accepted Answer

A) always change the optimal solution since the slope of the objective function changes. 
B) typically change the feasible region till a stage,beyond which the constraint functions become nonbinding. 
C) never change the optimal solution as the other coefficient is still fixed. 
D) change the optimal solution only if the slope of the objective function's contour changes significantly. 
E) their shadow prices although the constraints are not affected directly.

Question 16

The combination of decision variables optimizing a linear programming problem,occurs at:

Accepted Answer

A) a point where the objective function contour touches the feasible region. 
B) any point within the feasible region. 
C) any point outside the feasible region. 
D) any point where the constraint functions intersects the objective function. 
E) a point which will satisfy at least one of the constraints.

Question 17

A manufacturer of nutritional products is formulating a new liquid vitamin supplement.A bottle of the new product must contain at least 30 units of vitamin B and 50 units of vitamin C.A unit of vegetable extract (V)contains 1.2 units of vitamin B and 0.8 units of vitamin C.A unit of fruit extract (F)contains 0.25 units of vitamin B and 1.8 units of vitamin C.The cost of vegetable extract is $0.05 per unit and fruit extract costs $0.06 per unit.The firm's goal is to minimize its cost per bottle.Formulate a linear programming problem for the firm.

Accepted Answer

The answer of A manufacturer of nutritional products is formulating...

Question 18

The feasible region in a linear programming problem contains values of the decision variable that:

Accepted Answer

A) optimize the value of the objective function. 
B) are non-negative and finite in magnitude. 
C) satisfy only the nonbinding constraints 
D) satisfy all relevant constraints. 
E) are nonnegative.

Question 19

Given,MB = Marginal benefit and MC = Marginal cost.Then,for a positive decision variable in the optimal solution,which of the following relations holds?

Accepted Answer

A) MB = MC = 0 
B) MB - MC > 0 
C) MB - MC = 0 
D) MB - MC < 0 
E) MB - MC ≠ 0

Question 20

Determine the feasible region for the following linear programming problem:
Maximize Z = 10x + 8y
Subject to: 2x + 3y $\le$ 11
5x + 2y $\le$ 11;x,y $\ge$ 0

Accepted Answer

The answer of Determine the feasible region for the following...

Exam 17: Linear Programming