PLease help solve this word problem

Question

The point at which a​ company's profits equal zero is called the​ company's ​break-even

point.

Let R represent a​ company's revenue, let C represent the​ company's costs, and let x represent the number of units produced and sold each day.

R(x)=10x C(x)=6.5x+8,750

​(a) Find the​ firm's break-even​ point; that​ is, find x so that R=C.

​(b) Find the values of x such that R(x)>C(x). This represents the number of units that the company must sell to earn a profit.

Answer 1

(a) R=C

10x = 6.5x + 8750

10x - 6.5x = 8750

3.5x = 8750

x= 2500

(b) Let profit be p

since profit is calculated by subtracting costs from revenue, we can write p = R-C

At break-even p=0

so R-C = 0

so R=C

from part (a), we know that when R=C, x= 2500.

That is, at break-even, x = 2500

for profit, R(x) > C(x) and hence x>2500

Answer 2

a) R(x) = C(x)

10x = 6.5x + 8,750

3.5x = 8,750

x = 2,500

Breaking point = 10x = 25,000

b) x > 2,500 for R(x) > C(x)