The revenue function in terms of q will be 200q - 3q².
The following can be deduced based on the information given:
P(q) = 200 - 3q
C(q) = 75 + 80q - q²
The revenue function in terms of q will be:
= Price × Quantity
= (200 - 3q) × q
= 200q - 3q²
The profit will be:
= Total revenue - Total cost
= (200q - 3q²) - (75 + 80q - q²)
= 200q - 3q² - 75 + 80q + q²
= -2q² + 280q - 75
= 2q² - 280q + 75
The average cost function will be:
= Total cost / Quantity
= (75 + 80q - q²) / q
= 75/q + 80 - q
The marginal cost will be 80 - 2q.
The marginal revenue will be 200 - 6q.
The marginal cost when q = 20 will be:
= 80 - 2q
= 80 - 2(20)
= 80 - 40
= 40
The marginal revenue when q = 20 will be:
= 200 - 6q
= 200 - 6(20)
= 200 - 120
= 80
The company should decrease production from 20 units in order to gain more profit.
The production level that gives the largest profit for the company will be gotten by finding the second derivative for the profit function as illustrated in the question. The profit function is 2q² - 280q. Then the production level will be 4.
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