Implement the following LP problem in a spreadsheet. Use Solver to solve the problem and create a Sensitivity Report. Use this information to answer the following questions:

Max: 4x1 +2x2
Subject To: 2x1+4x2 <= 20
3x1+ 5x2<=15
x1, x2>=0

a. What range of values can the objective function coefficient for variable Xl assume without changing the optimal solution?
b. Is the optimal solution to this problem unique, or are there alternate optimal solutions?
c. How much does the objective function coefficient for variable X2 have to increase before it enters the optimal solution at a strictly positive level?
d. What is the optimal objective function value if X2 equals 1?
e. What is the optimal objective function value if the RHS value for the second constraint changes from 15 to 25?
f. Is the current solution still optimal if the coefficient forX2 in the second constraint changes from 5 to 1? Explain.

Question

07-03-2020
Mathematics

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Implement the following LP problem in a spreadsheet. Use Solver to solve the problem and create a Sensitivity Report. Use this information to answer the following questions:

Max: 4x1 +2x2
Subject To: 2x1+4x2 <= 20
3x1+ 5x2<=15
x1, x2>=0

a. What range of values can the objective function coefficient for variable Xl assume without changing the optimal solution?
b. Is the optimal solution to this problem unique, or are there alternate optimal solutions?
c. How much does the objective function coefficient for variable X2 have to increase before it enters the optimal solution at a strictly positive level?
d. What is the optimal objective function value if X2 equals 1?
e. What is the optimal objective function value if the RHS value for the second constraint changes from 15 to 25?
f. Is the current solution still optimal if the coefficient forX2 in the second constraint changes from 5 to 1? Explain.

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fortuneonyemuwa fortuneonyemuwa · Answer 1 · 2020-03-09T07:42:31+01:00

Answer:

The diagrams are uploaded accordingly as labelled

Step-by-step explanation:

The decision variables are given as [tex]X_1[/tex] and [tex]X_2[/tex]. Refer to the following screenshot for the objective function subject to the constraints as,

see fig 1

Now, in E8 and E9 use SUMPRODUCT() to calculate the used values based on decsision variables. The screenshots are as below.

see fig 2

Now, again use SUMPRODUCT() in cell F5 to calculate total value of the objective function, the screenshot is given as below

see fig 3

All the inputs have been done, hence click on the solve icon. A dialog box will appear. In the Target cell box, input F5, where the final result of objective function will appear. Also, select the max option box. In the text bx "By Changing cells", update the cell names where the actual numbers are to be updated. The screenshot is as shown below.

see fig 4

Now, define the contstarints in the text field named "Subject to Constraints". These constraints can be input by clicking on the Add button, and then a dialog box will appear. Define the first constraints by selcting the number field and assigning them as >=0. Click Add button. The screenshot is as shown below.

see fig 5

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