The Demand for cat food approximately satisfies the equation p=46-3x and the tot

Question

The Demand for cat food approximately satisfies the equation p=46-3x and the total cost of producing x units of cat food is C (x) =65+7x. (The quantity x is measured in thousands of pounds and the price and total cost are measured in hundreds of dollars.) Determine the level of production and the corresponding price that maximize the profit. The Demand for cat food approximately satisfies the equation p=46-3x and the total cost of producing x units of cat food is C (x) =65+7x. (The quantity x is measured in thousands of pounds and the price and total cost are measured in hundreds of dollars.) Determine the level of production and the corresponding price that maximize the profit.

Explanation / Answer

Profit, P(x) = px -C(x)

P(x) = 46x -3x2-65-7x = -3x2-65+39x

P '(x) = -6x+39

P '(x) =0

-6x+39=0

x = 39/6 = 6.5

p = 46-3x=46-3(6.5) = $26.50

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