Question

For a certain frozen pizza, as the cost goes from $2 to $4, the demand can be modeled by the formula y = -10x2 + 60x + 180, where x represents the cost and y represents the number of pizzas sold. Estimate the cost that will result in the greatest demand.

Answer 1

Answer:

The cost that will result in the greatest demand is $3

Step-by-step explanation:

Let

x ------> represents the cost  

y -----> represents the number of pizzas sold

we have

$y=-10x^{2}+60x+180$

This is a quadratic equation (vertical parabola) open downward

The vertex is a maximum

To find out the greatest demand calculate the vertex

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^{2}+k$

where

(h,k) is the vertex

Convert the quadratic equation in vertex form

Complete the squares

$y-180=-10x^{2}+60x$

Factor the leading coefficient

$y-180=-10(x^{2}-6x)$

$y-180-90=-10(x^{2}-6x+9)$

$y-270=-10(x^{2}-6x+9)$

Rewrite as perfect square

$y-270=-10(x-3)^{2}$

$y=-10(x-3)^{2}+270$ ----> equation in vertex form

The vertex is the point (3,270)

therefore

For the greatest demand

The cost is $3

The number of pizzas sold is 270