Question

For xyz manufacturing the fixed costs are $1200, material and labor costs combined are $2 per unit, and the demand equation is:

p=100/√q

What level of output will maximize profit? Show this occurs when marginal revenue equals marginal cost. What is the price at the profit maximization?

---

I understand R=p*q

R=100/√q * q =100/√q

I think
Profit = R-2q-1200

Then I don't know what to do.. Can anyone help?

Answer 1

You have a slight(!) error:
R = 100/√q * q = 100√q

Profit = R-2q-1200
= 100√q - 2q - 1200

maximum profit where dP/dq = 0

50/√q - 2 = 0
50 = 2√q
q = 625

since P = R-C,
dP/dq = 0 when dR/dq = dC/dq

The price is 100*25 = 2500