contestada

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.)

Respuesta :

lestat345

Answer:

The production level that maximizes Silky's profit is [tex]5000[/tex] ties.

Explanation:

Hi

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

[tex]P(Q)=\frac{150-Q}{0.2}=750-5Q[/tex]

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

The optimum level is when we have [tex]MC=I'(Q)[/tex], therefore,

[tex]5Q=750-10Q[/tex], as we clear it for [tex]Q[/tex] we find that

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

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