Exam 24: Linear Programming

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

All linear programming problems must have ______ distinct features.

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.

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?

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 aircraft plywood panels that Diamond Plywood will produce?

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.

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

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?

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 ______. Cell Name Final Value Shadow Price Constraint R . Side Allowable Increase Alowable Decrease \ 1\ 7 <= Usage 240 0.6 240 210 40 \ 1\ 8 <= Usage 150 3.2 150 30 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 ______.

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?

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

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 profit from hardwood plywood panels?

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.

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.If Diamond Plywood wishes to increase its capacity in one of the four operations,which operation should it be?

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

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

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? Nutrient Kidney Besns Tofu Minimum Daily Requirement Cost per pound \ 0.90 \ 1.50 Calcium in units per pound 15 6 30 Protein in units per pound 10 10 40 Calories in units per pound 3 9 18

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? Cell Name Final Value Shadow Price Constraint R . Side Allowable Increase Alowable Decrease \ 1\ 7 <= Usage 240 0.6 240 210 40 \ 1\ 8 <= Usage 150 3.2 150 30 70

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.