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?

The revenue for a company producing friendship bracelets is given fx 15x2 30x 200 where x is the price in dollars for each friendship bracelet The cost for the class=

Respuesta :

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

Cost is given by y = 5x - 12

to break even, then Revenue = Cost

Then:

[tex]-15x^2-30x+200=5x-12[/tex]

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

Step #1.

add 12 to both sides

[tex]-15x^2-30x+200+12=5x-12+12[/tex]

#2

Simplify

[tex]-15x^2-30x+212=5x[/tex]

#3

subtract 5x from both sides

[tex]-15x^2-30x+212-5x=5x-5x[/tex]

#4

Simplify

[tex]-15x^2-35x+212=0[/tex]

#5

Use the general formula to solve quadratic equation

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

#6

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

#7

[tex]x=-\frac{35+\sqrt{13945}}{30},\: x=\frac{\sqrt{13945}-35}{30}[/tex]

#8

in decimal numbers

[tex]x=-5.10,\: x=2.77[/tex]

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

d) $2.77

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