Question 965267
Must develop a quadratic function in order to solve the problem: A store sells
6000 gallons of paint each week for $15 per gallon. For each $1 decrease in the
price, the store will sell an additional 1000 gallons each week. What should the
sale price be to maximize the income?

<pre>
Let x = the number of dollar decreases.
Let y = the income with x dollars degreases.

For each $1 decrease in the price, the store will sell an additional 1000 gallons each week. 

Number of gallons sold after x dollar decreases = 6000 + 1000x
Price per gallon after x dollar decreases = $15-$x

Income = y = (6000+1000x)(15-x)
         y = 90000-6000x+15000x-1000x^2
         y = 90000+9000x-1000x^2
         y = -1000x^2+9000x+90000

Compare to

         y = ax^2+bx+c

a= -1000, b = 9000

Use vertex formula:

x-coordinate of vertex = -b/(2a) = -(9000)/(2*-1000) = -9000/(-2000) = 4.5

Therefore decreasing the price 4.5 dollar decreases, which means a reduction
of $4.50 will yield the maximum income.

So the sale price should be $15-$4.50 = $10.50 per gallon, to maximixe
income.

Edwin</pre>