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 the 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. Recall that the net income is the sales revenue minus the production cost.
(b) Solve the problem graphically to obtain an optimal solution.
(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?