SOLUTION: i. If the profit derived from producing x hundred units of a commodity is P = 4000(x − 2)(15 − x) dollars. a. Find P’(x).
b. Determine the level of output at whi
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Question 1111818: i. If the profit derived from producing x hundred units of a commodity is P = 4000(x − 2)(15 − x) dollars. a. Find P’(x).
b. Determine the level of output at which P’(x) = 0.
c. What is the economic significance of the level of production determined in part (b) above?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
P = 4000(x − 2)(15 − x)
:
P = 4000(-x^2 +17x -30) = -4000x^2 +68000x -120000
:
a) P' = -8000x +68000
:
b) -8000x +68000 = 0
:
-8000x = -68000
:
x = 8.5
:
level of production is 8.5 * 100 = 850 units
:
c) since the graph of P is a parabola which curves downward, 850 units represents the level of production that maximizes profit
:
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