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27 April, 08:39

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

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  1. 27 April, 09:57
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    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 = 2500 ... equation 1

    100a + 150b = 600,000 ... equation 2

    multiply equation 1 by 100 we have

    100a + 100b = 250000 ... equation 3

    Subtract equation 3 from 2

    100a + 150b = 600,000 ... equation 2

    100a + 100b = 250,000 ... equation 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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