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

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

Step-by-step 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)=(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=(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.