Question

Silky Inc., which sells custom silk ties designed by famous people, faces a demand curve of Q = 150 – 0.2P, where Q is measured in hundreds of ties and P is the price per tie. The marginal cost of production is given by MC = 5Q. What is Silky's profit-maximizing output level? (Hint: Add two zeros to the number you get.)

Answer 1

Answer:

The production level that maximizes Silky's profit is $5000$ ties.

Explanation:

Hi

First of all, as we have $Q(P)=150-0.2P$, we need to transcript it as price in function of the quantity so

$P(Q)=\frac{150-Q}{0.2}=750-5Q$

Then we need to find income function that is $I(Q)=Q*P(Q)=750Q-5Q^{2}$.  After derivate it $I'(Q)=750-10Q$.

The optimum level is when we have $MC=I'(Q)$, therefore,

$5Q=750-10Q$, as we clear it for $Q$ we find that

$Q=\frac{750}{15}=50$, finally as we have that $Q$ is measured in hundreds of ties, the production level that maximizes Silky's profit is $5000$ ties.