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- Aug 25th 2007, 02:49 PMMicka1compute income
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- Aug 25th 2007, 04:06 PMTKHunny
Price * Number Sold = Total Income.

x(y) = Price based on number sold = 400 - 0.3y

y = Number sold

y*x(y) = Total Income = z(y) = y*(400-0.3y) = 400y - 0.3y^2 - Sep 1st 2007, 09:24 PMTKHunny
z(y)=400y-0.3y^2

v(y)=4000+6y-.001y^2

$\displaystyle Profit(y) = z(y)-v(y) = 4000 + 394y - 0.299y^{2}$

What do you know about parabolas with negative leading coefficients?

Since you are to use Differential Calculus,

$\displaystyle \frac{dProfit}{dy} = -0.598y + 394$

Where is that zero?

-0.598y + 394 = 0 and Solve for y.

You are beginning to worry me. It seems as though you are a little too eager to give up on a problem if it does not immediately make sense. Maybe it would help to know why you are in this class. Have you had success in the prerequisite mathematics courses? - Sep 5th 2007, 05:45 AMtopsquark
What??

You solve

$\displaystyle \frac{d}{dy}(4000 + 394y - 0.299y^2) = -0.598y + 394 = 0$

to find the critical values of y, just as TKHunny showed you. Then you look at each of these y values in the original equation to see which is the minimum or maximum. (Or you can use the second derivative test.)

-Dan