Question

National Business Machines manufactures two models of fax machines: A and B. Each model A costs $120 to make, and each model B costs $160. The profits are $29 for each model A and $38 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2900 and the company has earmarked no more than $550,000/month for manufacturing costs, how many units of each model should National make each month in order to maximize its monthly profit?

Answer 1

Let,

number of units of A to produce = x1
number of units of B to produce = x2

Objective function = Max 29x1+38x2

Subject to,

120x1+160x2 <= 550000 (Cost constraint)
x1+x2 <= 2900 (Total number of fax machines models)

x1,x2 >= 0 (Non-negativity constraint)

Solving in excel solver we get,

number of units of A to produce = x1 = 0
number of units of B to produce = x2 = 2900

maximized profit = 110200

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