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3 October, 15:51

Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, R (x), and cost, C (x), of producing x units are in dollars.

R (x) = 60x-.5x^2 and C (x) = 4x+20

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  1. 3 October, 16:08
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    The maximum profit at x = 5.6 units is

    Pmₐₓ = 136.8 per unit cost

    Step-by-step explanation:

    Explanation:-

    Given Revenue function R (x) = 60x-.5x^2 and

    Given the cost function is C (x) = 4x+20

    Profit = R (x) - C (x)

    profit = 60x-.5x^2 - (4x+20)

    = 60x - 5x^2 - 4x - 20

    P = 56x - 5x^2 - 20 ... (i)

    Now differentiating equation (1) with respective to 'x'

    P¹ = 56 - 5 (2x) - 0

    P¹ = 56 - 10x

    The derivative of profit function is equating zero

    56 - 10x = 0

    56 = 10x

    x = 5.6

    The maximum profit at x = 5.6

    Pmₐₓ = 56x - 5x^2 - 20

    = 56 (5.6) - 5 (5.6) ^2-20

    = 136.8

    Final answer:-

    The maximum profit at x = 5.6 units is

    Pmₐₓ = 136.8 per unit cost
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