Question

The demand equation for a monopolistic firm’s product is 4p+q= 320, and the firm’s cost function is given by c = 0.1q2+ 10q+ 1500. Find the price that maximizes the firm’s profit. What is the firm’s profit?

Answer 1

Answer:

price =100 and profit is $2000

Step-by-step explanation:

The demand equation for a monopolistic firm’s product is 4p+q= 320

Solve for p

$4p+q= 320$

$4p=-q+320$, divide both sides by 4

$p=-\frac{q}{4}+80$

Revenue function R= p times q

$R=p \cdot q=-\frac{q^2}{4}+80q$

$C= 0.1q^2+ 10q+ 1500$

Profit = Revenue - Cost

$Profit=-\frac{q^2}{4}+80q-(0.1q^2+ 10q+ 1500)$

$Profit P(q)=-0.35q^2+70q-1500$

to find maximum profit find out vertex

$q=\frac{-b}{2a} =\frac{-70}{2(0.35)} =100$

Plug in 100 for q inf P(q)

$Profit P(100)=-0.35(100)^2+70(100)-1500=2000$

price =100 and profit is $2000