(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Through market research, a computer manufacturer found that x thousand

units of its new laptop will sell at a price of 2000 - 5x dollars per unit.

The cost, C, in dollars of producing this many units is

C(x) = 15 000 000 +1 800 000x + 75x^2. Determine the level of sales

that will maximize profit.

2. Relevant equations

Profit = Revenue - Cost

3. The attempt at a solution

I said Revenue = 2000 - 5x and Cost = 15 000 000 +1 800 000x + 75x^2

Using the formula Profit = Revenue - Cost I subtracted them from each other and got:

Profit = -14998000 - 1800005x - 75x^2

Then I found the derivative which came out to be:

P'(x) = -1800005 - 150x

Then I set it equal to zero and solved for x:

0 = -1800005 - 150x

1800005 = -150x

x = -12000.03

but the answer in the back of the book is 19 704 units.

Can anyone explain what I did wrong?

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# Homework Help: Optimization: Maximizing Profit

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