Question

The revenue for a company producing friendship bracelets is given f(x) = -15x^2 - 30x + 200, where x is the price in dollars for each friendship bracelet. The cost for the production is given by y = 5x - 12. What price should the company sell the friendship bracelets to break even?

Answer 1

Revenue is given by f(x) = -15x^2 - 30x + 200

Cost is given by y = 5x - 12

to break even, then Revenue = Cost

Then:

$-15x^2-30x+200=5x-12$

Now, let's solve for x, which is the price

Step #1.

add 12 to both sides

$-15x^2-30x+200+12=5x-12+12$

#2

Simplify

$-15x^2-30x+212=5x$

#3

subtract 5x from both sides

$-15x^2-30x+212-5x=5x-5x$

#4

Simplify

$-15x^2-35x+212=0$

#5

Use the general formula to solve quadratic equation

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a};a^2x+bx+c=0$$x_{1,\: 2}=\frac{-\left(-35\right)\pm\sqrt{\left(-35\right)^2-4\left(-15\right)\cdot\:212}}{2\left(-15\right)}$

#6

$x_1=\frac{-\left(-35\right)+\sqrt{13945}}{2\left(-15\right)},\: x_2=\frac{-\left(-35\right)-\sqrt{13945}}{2\left(-15\right)}$

#7

$x=-\frac{35+\sqrt{13945}}{30},\: x=\frac{\sqrt{13945}-35}{30}$

#8

in decimal numbers

$x=-5.10,\: x=2.77$

a negative value does not make sense in this case, therefore the answer is

d) $2.77