Mark M. answered • 09/30/20
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Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.
Marginal revenue is the derivative of revenue, R(x), where x is the number of units sold.
So, R(x) = ∫ 25x dx = 12.5x2
Marginal cost is the derivative of cost, C(x). So, C(x) = ∫[100 / (x+4)1/2]dx = 200√(x+4) + k (k = a constant)
Since C(0) = 1200, we have 400 + k = 1200. So, k = 800.
Therefore, C(x) = 200√(x+4) + 800.
P(x) = profit if x units are produced and sold = R(x) - C(x) = 12.5x2 - 200√(x+4) - 800
Thus, P(10) = 1250 - 200√14 - 800 = -$298.33 (there is a loss of $298.33 when x = 10)
Anthony F.
To get the revenue function, the indefinite integral of the marginal revenue function was calculated. To get the cost function, the indefinite integral of the marginal cost function was calculated and profit was calculated by subtracting the cost from revenue. In this case, no profit made only a loss for the 10 units produced and sold.09/30/20