Exam 24: Linear Programming

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?

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?

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.

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

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

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

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

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 tropical plywood panels?

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?

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 soft plywood panels?

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.

______ 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.

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?

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 aircraft 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.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?

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?

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

______ helps in the determination of how sensitive the current optimal solution is to changes in the input parameter values.

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

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