Aschool typically sells 500 yearbooks each year for $50 each. the economics class does a project and discovers that they can sell 125 more yearbooks for every $5 decrease in price. the revenue for the school sales is r(x)=(500+125x)(50-5x) to maximize profit, what price should the school charge for the yearbooks? what is the possible maximum revenue? if the school attains the maximum revenue, how many yearbooks will they sell?

$35 per yearbook; $30,625

Step-by-step explanation:

In this function, x represents the number of $5 decreases.  To find the vertex, we first find the axis of symmetry.  We will first write this function in standard form, by multiplying:

R(x) = (500+125x)(50-5x)

= 500(50)+500(-5x)+125x(50)+125x(-5x)

= 25000+-2500x+6250x-625x²

= 25000+3750x-625x²

= -625x²+3750x+25000

The axis of symmetry is found using the formula

x = -b/2a

x = -3750/2(-625) = -3750/(-1250) = 3

Next we use this value of x to find the y-coordinate of the vertex.  We substitute this into the function:

R(3) = -625(3²)+3750(3)+25000

= -5265+11250+25000 = 30625

This makes the vertex (3, 30625).  This means with 3 $5 decreases, the revenue will be $30,625.

3 $5 decreases means decreasing 3(5) = $15 from the price.  This means they sell the yearbooks for 50-15 = $35.

center= (-2,0)

radius= sqrt2/2

step-by-step explanation: