National Business Machines manufactures two models of fax machines: A and B. Each model A costs $100 to make, and each model B costs $150. The profits are $30 for each model A and $40 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2500 and the company has earmarked no more than $600,000/month for manufacturing costs, how many units of each model should National m

4500 units of A and 7,000 units of B

Explanation:

The linear programming equations can be formed as:

The objective function = 30a + 40b

a + b = 2500equation 1

100a + 150b = 600,000equation 2

multiply equation 1 by 100 we have

100a + 100b = 250000equation 3

Subtract equation 3 from 2

100a + 150b = 600,000equation 2

100a + 100b = 250,000equation 3

              50b = 350,000

Therefore b = 350,000 / 50 = 7,000

substitute 7000 for b in equation 1

a + 7000 = 2500

a = 2,500 - 7000 = 4500 (ignoring the minus sign)

Therefore the company should produce 4500 units of A and 7,000 units of B

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