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mezya [45]
3 years ago
11

A fertilizer producer finds that it can sell its product at a price of dollars per unit when it produces units of fertilizer. Th

e total production cost (in dollars) for units is If the production capacity of the firm is at most 1000 units of fertilizer in a specified time, how many units must be manufactured and sold in that time to maximize the profit?
Biology
1 answer:
Vilka [71]3 years ago
5 0

Answer:

700

Explanation:

If from the question the price per unit of fertilizer, p(x) = 300 - 0.1x

The cost of x units of  fertilizer = C(x) = 15000 + 125x + 0.025x^2

And we know that Profit = Revenue - Cost

Revenue for x units of fertilizer R(X) = x*p(x)

= 300x - 0.1x^2

Hence Profit: P(x) = R(x) - C(x)

= [300x - 0.1x^2] - [15000 + 125x + 0.025x^2]  

= -0.125x^2 + 175x - 15000

To determine critical values

P'(x) = -0.25x + 175 = 0

Thus x = 175/0.25

x = 700

To maximize profit, the manufactures must produce 700 units of fertilizers

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