Question

Reconsider the Wyndor Glass Co. case study introduced in Section 2.1/ in class. Suppose that the estimates of the unit profits for the two new products now have been revised to $500 for the doors and $350 for the windows. (The number of the products are required to be integer.)

a. Formulate this same model algebraically. (Please clearly define all the decision variables, clearly write down the objective function and each constraints)
b. Formulate and solve the revised linear programming model for this problem on a spreadsheet.

Answer 1

a)

Algebraic linear programming model is following:

Decision variables:  

Let D be the number of Doors to be produced (or production rate of doors), and

W be the number of Windows to be produced.

.

Objective function:

Max 500D + 350W - 25D² - 66W²

.

Constraints:

1D + 0W <= 4

0D + 2W <= 12

3D + 2W <=18

D, W >= 0

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b)

Formulate Spreadsheet model as follows:

Note that marketing cost is quadratic function. Therefore, it is a nonlinear model.

In Solver Parameters, Select a Solving Method: GRG Nonlinear

Enter Solver Parameters as shown below:

Click Solve to generate the solution.

After that, values appear automatically in variable cells, B7:C7

Click OK

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Number of Doors to be produced, D = 4

Number of Windows to be produced, W = 2.65

Total net profit = $ 2064.015   (this is net of marketing cost)

NOTE - HYPOTHETICAL FIGURES ARE TAKEN BECAUSE THERE IS NO FIGURES GIVEN