Question

44. Consider the following linear program Max 1a+1b s.t. 5a+3b<15 3a+5b,<15 a,b >0 A. What is the optimal solution for this problem? B. Suppose that the objective function is changed to 1a+2b. Find the new optimal solution. I am using excel for this homework question so I need the formulas to help not just the answers and I also trying to figure desmos to graph the question.

Answer 1

Answer:

a = 1.875

b = 1.875

Explanation:

The LP is solved using the excel solver by following these steps,

Step 1: Write the decision variable with value zero. The screenshot is shown below

Step 2: Write the objective function equation while taking the decision variable value. The screenshot is shown below,

Step 3: Write the constraints equation while taking the decision variable value and write the right side value of the constraint

The screenshot for constraint 1 is shown below,

The screenshot for constraint 2 is shown below,

The screenshot for non-negativity constraints 3 and 4 is shown below,

Step 4: (If you have not install the solver excel follow, FILE > Options > Add-ins > Manage: select ExcelAdd-ins > Go then tick Solver Add-in > OK)

DATA > Solver > OK. The screenshot is shown below,

Step 5:

Set Objective: Select objective value,

To: select Max

Subject to the Constraints > Add > in Cell Reference select constraint value and in Constraint: select right hand side value of constraint and select the >= inequality.

Tick Make Unconstrained Variables Non-Negative

Select a Solving Method: Simplex LP

then click Solve. The screenshot is shown below,

Step 6: Select Reports > Answer then Ok

The result is obtained. The screenshots are shown below,

The Answer Report

Plot in Desmos

The screenshot is shown below,

Since this is a maximization problem, the objection function will move upward and the solution will lie on oneof the corner point.