Question 167518: A firm can sell X units of a product at a price of P cents per unit, where P = 503 - X
The total costs of production is given by the function T(X) = 500 + 2X.
# Find the number of units to be sold to achieve maximum profit and find the maximum profit.
# What price per unit would the firm be charging at the maximum profit output level?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A firm can sell X units of a product at a price of P cents per unit, where P = 503 - X
The total costs of production is given by the function T(X) = 500 + 2X.
# Find the number of units to be sold to achieve maximum profit and find the maximum profit.
# What price per unit would the firm be charging at the maximum profit output level?
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Revenue = price*# of units sold
Revenue = (503-x)(X) = 503x - x^2
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Cost = 500+2x
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Profit = [Revenue - Cost] = (503x-x^2)-(500+2x) = -500+501x-x^2
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Maximum profit occurs when x = -b/2a = -501/(2*-1) = 250.5
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Maximum profit will be -500 + 501*250.5-250.5^2 = $62,250.25
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Price when profit is maximum = 503-250.5 = $252.50
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Cheers,
Stan H.
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