A firm can produce 100 units per week. If its total cost function is $C = 600 + 1200 x$ dollars, and its total revenue function is $R = 1300 x - x ^ { 2 }$ dollars, how many units x should it produce to maximize its profit?
A)1250 units
B)650 units
C)93 units
D)50 units
E)100 units

Question

Quizplus · Accepted Answer

To maximize profit, set the derivative of the profit function $P(x) = R(x) - C(x)$ to zero. The profit function is $P(x) = (1300x - x^2) - (600 + 1200x)$. Simplifying gives $P(x) = 100x - x^2 - 600$. The derivative is $P'(x) = 100 - 2x$. Setting $P'(x) = 0$ gives $x = 50$.

A Firm Can Produce 100 Units Per Week C=600+1200xC = 600 + 1200 xC=600+1200x

A Firm Can Produce 100 Units Per Week $C = 600 + 1200 x$