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
