- #1
molly16
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Homework Statement
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.
Homework Equations
Profit = Revenue - Cost
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?