Question

Using a System to Break Even

A company’s weekly revenue, in thousands, is modeled by the equation R = -p2 + 14p, where p is the price of the product it makes. The company is considering hiring an outside source to distribute its products, which will cost the company 4p + 24 thousand dollars per week.


Part B
Create a system of equations for the break-even point(s) of the company’s product to assist with the decision of hiring the distributor. Assume the distributor’s cost is the only cost that needs to be considered.

Answer 1

Answer: P^2 - 10p + 24 = 0

Explanation:

Given that a company’s weekly revenue, in thousands, is modeled by the equation

R = -p2 + 14p,

where p is the price of the product it makes. The company is considering hiring an outside source to distribute its products, which will cost the company 4p + 24 thousand dollars per week.

If the company want to break even, the cost of hiring distributors will be equal to the revenue per week.

Therefore,

-P^2 + 14p = 4p + 24

Collect the like terms

-P^2 + 14p - 4p - 24 = 0

-P^2 + 10p - 24 = 0

Multiply all by minus sign

P^2 - 10p + 24 = 0