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Integration and profit maximization

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Q#16)
Suppose that the price-demand equation is given by p = 9 - ln x, where 0 < x <= 200, x is in thousands, and the cost of manufacturing is $3 per item. What price will maximize profit?

$2.00
$2.60
$3.00
$3.20
$4.00
$4.50
none of these

Q#17)

&#8747;(2 * sqrt(x^3) + 5x^-11 - 1/x) dx =

6/5 x^(5/3) - 1/(2x^10) - ln |x| + C
10/3 x^(5/3) - 1/(2x^10) - ln |x| + C
1/5 x^(5/2) - 1/(2x^10) - ln |x| + C
4/5 x^(5/2) - 1/(2x^10) - ln |x| + C
6/5 x^(5/3) - 5/(12x^12) - ln |x| + C
10/3 x^(5/3) - 5/(12x^12) - ln |x| + C
1/5 x^(5/2) - 5/(12x^12) - ln |x| + C
4/5 x^(5/2) - 5/(12x^12) - ln |x| + C
none of these

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Solution Summary

This provides an example of integration and an example of maximization of profit.

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Suppose that the price-demand equation is given by p = 9 - ln x, where 0 < x <= 200, x is in thousands, and the cost of manufacturing is $3 per item. What ...

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