Question

A company that manufactures hair ribbons knows that the number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation below.
x = 1,000 − 100p
At what price should the company sell the ribbons if it wants the weekly revenue to be $1,600? (Remember: The equation for revenue is R = xp.)
p = $ (smaller value)
p = $ (larger value)

Answer 1

Given:

The number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation:

$x=1000-100p$

To find:

The selling price if the company wants the weekly revenue to be $1,600.

Solution:

We know that the revenue is the product of quantity and price.

$R=xp$

$R=(1000-100p)p$

$R=1000p-100p^2$

We need to find the value of p when the value of R is $1600.

$1600=1000p-100p^2$

$1600-1000p+100p^2=0$

$100(16-10p+p^2)=0$

Divide both sides by 100.

$p^2-10p+16=0$

Splitting the middle term, we get

$p^2-8p-2p+16=0$

$p(p-8)-2(p-8)=0$

$(p-8)(p-2)=0$

Using zero product property, we get

$p-8=0$ or $p-2=0$

$p=8$ or $p=2$

Therefore, the smaller value of p is $2 and the larger value of p is $8.