A picture frame company produces four types of frames. Each type requires a certain amount of skilled labor, metal, and glass as shown in the table below. The unit selling price of each type is also shown in the table. During the coming week, the company can purchase up to 4,000 hours of skilled labor, 6,000 ounces of metal, and 10,000 ounces of glass. The unit costs are $8 per labor hour, $0.5 per ounce of metal, $0.75 per ounce of glass. Also, market constraints are such that it is impossible to sell more than 1000 type 1 frames, 2000 type 2 frames, 500 type 3 frames, and 1000 type 4 frames. a) Formulate a linear programming model that maximizes the company’s weekly profit and put it in standard format. (clearly define any decision variables and constraints).
b) Solve the problem using Excel solver to find the optimal solution
c) Based on your solution and sensitivity analysis, if you need to drop one of the products, which one would it be and why
d) Based on your solution and sensitivity analysis, what is the most valuable resource and why
Skilled Labor Metal Glass Selling Price
Frame 1 2 4 6 $ 28.50
Frame 2 1 2 2 $ 12.50
Frame 3 3 1 1 $ 29.25
Frame 4 2 2 2 $ 21.50