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21 August, 18:27

A factory cam produce two products, x and y, with a profit approximated by p=14x+22y-900. The production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the formula x+2y≤1600. What production levels yield maximum profit?

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  1. 21 August, 21:54
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    Solution : - Given a factory can produce two products x and y with profit approximated by p (x) = 14 x + 22 y - 900

    The production of y can exceed x by no more than 200 units. So the required constraints are

    y - x < 200 [equation 1]

    We draw the graph of equation 1 using table 1 as shown in figure.

    and

    x + 2 y ≤ 1600 [equation 2]

    We draw the graph of equation 2 using table 2 as shown in figure.

    Total profit p (x) = 14 x + 22 y - 900

    The mathematical formulation of the given problem is

    Maximize p (x) = 14 x + 22 y - 900

    Subject to the constraints

    y - x < 200 x + 2 y ≤ 1600 As we can see the table 3 the maximum profit is $21500 at (1600,00). So a production of 1600 of x and 0 of y gives the maximum profit of $21500
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