The cost to produce x units of wire is C = 60x + 660, while the revenue is R = 85x. Find all intervals where the product will at least break even.

Answer 1

Revenue R is the amount of money taken in by selling a product. Cost C is how much is spent producing the product.

You want to find where R - C >= 0. When R-C = 0 then revenue exactly matches cost. Otherwise when R > C then profit is made.

Solve for 85X - (60X + 660) = 0

85X - 60X - 660 = 0

(85-60)X - 660 = 0

25X - 660 = 0

25X = 660

X = 660/25 = 26.4

Revenue will exactly match Cost when 26.4 units of wire are produced. This is the break-even value of X.

When X > 26.4, R - C > 0 indicating a profit is being made.

The interval of interest is [26.4, oo). Note oo stands for + infinity