Answer to Question #215658 in Microeconomics for fafa

Question #215658

Some years ago, it was estimated that the demand for steel approximately satisfied the equation P = 256 - 50x

And the total cost of producing x units of steel was C(x) = 182 + 56x

Determine the level of production and the corresponding price that maximize the profits.



1
Expert's answer
2021-07-14T11:59:44-0400

"Profit, P(x) = R(x)-C(x)"

"P(x) = x(256-50x)-(182+56x)"

"P(x) = 256x-50x2-182-56x"

"P(x) = -50x2+200x-182"

"P '(x) = -100x+200"

"P'(x)=0"

"-100x+200=0"

"x=2"

So level of production is 2 million of tons

p=256-50(2)=156 million of dollars


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