Question 1147464
r(x) = .75 * x
r(x) is the revenue.
x is he number of pencils sold.


you are given that it costs the company 3500 to produce 3000 pencils and that it costs the company 1500 a month even if they don't produce any pencils.


your cost equation is c(x) = 1500 + p * x
c(x) is the cost.
p is price per pencil
x is the number of pencils.



you can see that, when x = 0, the cost is 1500.
that's a flat expense that they have to pay every month in addition to the cost of producing any pencils.


you are given that the cost is 3500 when 3000 pencils are produced.
c(x) = 1500 + p * x becomes 3500 = 1500 + p * 3000
subtract 1500 from both sides of this equation to get:
2000 = p * 3000
divide both sides of this equation by 3000 and solve for p to get:
p = 2/3 of a dollar each = $.666666666..... each.


to break even, r(x) must be equal to c(x).
you get:
.75 * x = 1500 + 2/3 * x
i'll work in fractions, so the formula becomes:
3/4 * x = 1500 + 2/3 * x
subtract 2/3 * x from both sides of this equation to get:
3/4 * x - 2/3 * x = 1500
place all fractions under a common denominator to get:
9/12 * x - 8/12 * x = 1500
combine like terms to get:
1/12 * x = 1500
solve for x to get:
x = 1500 * 12/1 = 18000


the company will break even when 18000 pencils are sold.
r(x) = .75 * 18000 = 13500
c(x) = 1500 + 2/3 * 18000 = 13500
revenue = cost = break even point.