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.
"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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