Exam 24: Linear Programming

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?

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

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

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.

Changing the value of the objective coefficient will change ______.

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?

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?

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

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 reduce its capacity in one of the four operations,which one should it avoid?

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?

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?

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

A school is trying to determine a nutritional diet to feed its students.The school would like to offer some combination of milk and beans.The school's 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. Nutrient Kidney Beans 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 At the optimum solution,what is the total number of units of protein included in the diet?

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.

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 school is trying to determine a nutritional diet to feed its students.The school would like to offer some combination of milk and beans.The school's 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. Nutrient Kidney Beans 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 At the optimum solution,what is the total number of units of calcium included in the diet?

A school is trying to determine a nutritional diet to feed its students.The school would like to offer some combination of milk and beans.The school's 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. Nutrient Kidney Beans 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 At the optimum solution,what is the cost of kidney beans in the diet?

The resource constraints are modeled in LP mathematically as ______.

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 ______.