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  3. 1. a company produces and sells two di?erent produ

1. A company produces and sells two di?erent products. The demand for each product is unlimited,...

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Advance Math

1. A company produces and sells two di?erent products. Thedemand for each product is unlimited, but the company isconstrained by cash availability and machine capacity. Each unit ofthe ?rst and second product requires 3 and 4 machine hours,respectively. There are 20,000 machine hours available in thecurrent production period. The production costs are $3 and $2 perunit of the ?rst and second product, respectively. The sellingprices of the ?rst and second product are $6 and $5.40 per unit,respectively. The available cash is $4,000 and furthermore, 45% ofthe sales revenues from the ?rst product and 30% from the secondproduct will be made available to ?nance operations during thecurrent period.
(a) Formulate an LP problem that maximizes the company’s net incomesubject to cash availability and machine capacitylimitations.
(b) Solve the problem graphically to obtain an optimalsolution.
(c) Suppose that the company could increase its suitable machinehours by 2,000 after spending $400 for certain repairs. Should theinvestment be made?

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