Question

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.

Answer 1

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

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

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

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

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

$P'(x)=0$

$-100x+200=0$

$x=2$

So level of production is 2 million of tons

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