A company produces and sells two different products. The demand for each product is unlimited

A company produces and sells two different products. The demand for each product is unlimited, but the company is constrained by cash availability and machine capacity. Each unit of the first and second product requires 3 and 4 machine hours, respectively. There are 20,000 machine hours available in the current production period. The production costs are $3 and $2 per unit of the first and second product, respectively. The selling prices of the first and second product are $6 and $5.40 per unit, respectively. The available cash is $4,000: furthermore. 45% of the sales revenues from the first product and 30% of the sales revenues from the second product will be made available to finance operations during the current period. (a) Formulate a linear programming problem that aims at maximizing net income subject to the cash availability and machine capacity limitations. Clearly indicate your decision variables, your objective function, and your constraints. (b) Solve this in Excel. Attach the Answer Report to your HW. Be sure to indicate on it if you worked with anyone else. (c) Suppose that the company could increase its available machine hours by 2,000, after spending $400 for certain repairs. Should the investment be made?

Expert Answer


a) Below is teh formulation and calculation –

Objective Function

Maximize Net income Z = (6-3)P1+(5.4-2)P2 = 3P1+3.4P2

subject to constraints –

Machine hours — 3P1+4P2 <= 20000

Cash —– 3P1+2P2 <= 4000+0.45*(6P1)+0.3*(5.4P2) => 0.3P1+0.38P2 <=4000

Non-negativity constraint — P1,P2 >=0

b) Solving the above equations through Excel solver, the net income = 17000 $

c) Below is the calculation based on the increase in machine hours and after spending cash for repairs.

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