Answer:
The price that maximizes profits is $230 per good
The maximum profits earned at the above set price is $2,180,000
Step-by-step explanation:
Determine the profit function
[tex]Q=70000-200P\\Q+200P=70000\\200P=70000-Q\\P=350-\frac{1}{200}Q[/tex]
Find the total revenue function
[tex]TR=P*Q\\TR=(350-0.005Q)*Q\\TR=350Q-0.005Q^2[/tex]
Find the total profit function
[tex]TP=TR-TC\\TP=(350Q-0.005Q^2)-(110Q+700000)\\TP=240Q-0.005Q^2-700000[/tex]
Determine the profit-maximizing quantity of output
[tex]\frac{d(PT)}{dQ}=240-0.01Q[/tex]
[tex]0=240-0.01Q[/tex]
[tex]-240=-0.01Q[/tex]
[tex]24000=Q[/tex]
Determine the profit-maximizing price
[tex]P=350-0.005Q\\P=350-0.005(24000)\\P=350-120\\P=230[/tex]
(Optional) Determine the total profit
[tex]TP=240Q-0.005Q^2-700000\\TP=240(24000)-0.005(24000)^2-700000\\TP=2180000[/tex]
This means that the firm makes its maximum profit of $2,180,000 when the price per good is set to $230.
