Answer to Question #157350 in Calculus for Shahnawaz Rehman

Question #157350

The annual profit for the firm depends upon the number of units produced. Specifically the function which describes the relationship between profit P (stated in dollars) and the number of units produced x is

P=-0.01x^2+5000x-25000

a) Determine the number of units x which will result in maximum profit.

b) What is the expected maximum profit?


1
Expert's answer
2021-01-25T00:06:13-0500

Given that

P=0.01x2+5000x25000P = -0.01x^{2} + 5000x - 25000

Then we have that dPdx=0.02x+5000\frac{dP}{dx} = -0.02x + 5000

So when dPdx=0\frac{dP}{dx} = 0

We have that 0.02x+5000=0-0.02x + 5000 = 0

0.02x=50000.02x = 5000

x=50000.02x = \frac{5000}{0.02}

x=250000x = 250000

So the answer to question (a) is that 250000 will result in the maximum profit

b) So we substitute the value of x=250000x = 250000 into P=0.01x2+5000x25000P = -0.01x^{2} + 5000x - 25000

So we have that P(250000)=P(250000) = 0.01(250000)2+5000(250000)25000-0.01(250000)^{2} + 5000(250000) - 25000

P(250000)=624975000P(250000)= 624975000

The expected maximum profit is 624975000



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