The price/output combination at which total profit is maximized is P = $830 and Q = 700 units. At that point, MR = MC and total profit is maximized at $209,000.
The price/output combination at which average cost is minimized is P = $870 and Q = 300 units. At that point, MC = AC = $440.
C. To find the profit-maximizing output level analytically, set MR = MC, or set Mn = 0, and solve for Q. Because
= ($900Q - $0.1Q2)/Q = $900 - $0.1(700) = $830 n = TR - TC
= $900Q - $0.1 Q2 - $36,000 - $200Q - $0.4Q2 = -$36,000 + $700(700) - $0.5(7002) = $209,000
(Note: This is a profit maximum because profits are falling for Q > 700.)
To find the average-cost minimizing output level, set MC = AC, and solve for Q. Because
= ($36,000 + $200Q + $0.4Q2)/Q = $36,000Q-i + $200 + $0.4Q
it follows that
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