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12 May, 07:28

A firm has monthly average costs, in dollars, given by C = 43,000 x + 200 + x where x is the number of units produced per month. The firm can sell its product in a competitive market for $1800 per unit. If production is limited to 200 units per month, find the number of units that gives maximum profit.

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  1. 12 May, 07:53
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    x = 800

    but the production of units is limited to 200 units hence profit is not possible with given constraint

    Explanation:

    Given dа ta:

    average cost is = 43000/x + 200 + x, here x denote number of unit

    cost of per unit = $1800

    total unit produced in one month is 200

    Profit can be calculated as

    Profit = revenue - cost

    P = 1800 - (43000/X + 200 + X)

    P X = 1800 X - 43000 - 200X - X^2

    PX = - X^2 + 1600 X - 43000

    P'X = - 2X + 1600X

    P'X = 0

    x = 800

    but the production of units is limited to 200 units hence profit is not possible with given constraint
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