1. optimization - maximizing profit

the sale price of an item is 800-35x dollars and the total manufacturing cost is $\displaystyle 2x^3-140x^2+2,600x+10,000$ dollars, where x is the number of items. What number of items should be manufactured in order to optimize the manufacturer's total profit?

2. Originally Posted by yoman360
the sale price of an item is 800-35x dollars and the total manufacturing cost is $\displaystyle 2x^3-140x^2+2,600x+10,000$ dollars, where x is the number of items. What number of items should be manufactured in order to optimize the manufacturer's total profit?
Profit = Revenue - Cost = $\displaystyle (800-35x)-(2x^3 - 140x^2 + 2600x + 10000)$

Just differentiate and find the max.

3. Originally Posted by Gusbob
Profit = Revenue - Cost = $\displaystyle (800-35x)-(2x^3 - 140x^2 + 2600x + 10000)$

Just differentiate and find the max.
I tried that and but it does not have a max. i even graphed it on calculator and the derivative does not cross x-axis

4. Originally Posted by yoman360
I tried that and but it does not have a max. i even graphed it on calculator and the derivative does not cross x-axis
Try again and make sure the signs are correct.

Wolfram|Alpha

5. Originally Posted by Gusbob
Try again and make sure the signs are correct.

Wolfram|Alpha
Thanks. i just made a stupid mistake

optimize the manufacturer's total profit

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