Find the maximum profit corresponding to a demand function of p = 36 − 4 x and a total cost function = 2 x 2 + 6Hello. Can you kindly help me solve this problem? Thank you in advance

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Find the maximum profit corresponding to a  demand function of      p  =  36  −  4  x and a total   cost     function     =  2      x    2    +  6Hello. Can you kindly help me solve this problem? Thank you in advance

owerswogsnz · Accepted Answer

Profit = Income - Costs.I assume x is the price per unit and p the number of units sold. That means Income is the number of units sold times the price per unit:  Profit  =  (  36  −  4  x  )  ×  x  −  (  2      x    2    +  6  )So the profit function is a quadratic expression and therefor has a turning point (vertex) as a graph, which represents the maximum value. This occurs when the gradient is 0, and the derivative is a formula for the gradient. So by making             d      (Profit)              d      x        =  0 and solving x, that will give me at what price I will have a maximum profit. Substituting into Profit will give the maximum profit.NOTE: Of course any other method of finding the vertex of a parabola should produce the same answer.

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