Maximizing price and quantity

[gary_]

I need my answers checked, thanks so much, please point out my mistakes.

Demand:
P=1800-0.006Q
Average cost: 12,100,000/Q +800 +0.004Q

a) Calculate price and quantity that maximize revenue
Revenue=pq
R=1800Q-0.006Q^2
dR/dQ=1800-0.012Q=0
Q=150,000
P=1800-0.006(150,000)
P=900

b) Calculate price and quantity that miximize profit
Profit=TR-TC
P=(1800-0.006Q)-(12,100,000 +800Q +0.004Q^2)
P=-12,100,000+1000Q-0.01Q^2
dP/dQ=1000-0.02Q=0
Q=50,000
P=1800-0.006(50,000)
P=1500

 

[skeeter]

I need my answers checked, thanks so much, please point out my mistakes.

Demand:
P=1800-0.006Q
Average cost: 12,100,000/Q +800 +0.004Q

a) Calculate price and quantity that maximize revenue
Revenue=pq
R=1800Q-0.006Q^2
dR/dQ=1800-0.012Q=0
Q=150,000
P=1800-0.006(150,000)
P=900

b) Calculate price and quantity that miximize profit
Profit=TR-TC
P=(1800-0.006Q)-(12,100,000 +800Q +0.004Q^2)
should be P = (1800Q - 0.006Q²) - (12,100,000 +800Q +0.004Q²) ... next step is correct
P=-12,100,000+1000Q-0.01Q^2
dP/dQ=1000-0.02Q=0
Q=50,000
P=1800-0.006(50,000)
P=1500

 

[gary_]

thanks for catching that.