Question

The revenue (in millions of dollars) from the sale of x units at a home supply outlet is given by R(x) = .21x. The profit (in millions of dollars) from the sale of x units is given by P(x) = .084x - 1.5. a. Find the cost equation. b. What is the cost of producing 7 units? c. What is the break-even point?

Answer 1

Answer: a) C = 0.126x + 1.5

b) C = 2.382 c) approximately 179 units

Step-by-step explanation: profit P(x), total revenue R(x) and total cost (C) are related by the formulae below.

Profit = total revenue - total cost

P(x) = R(x) - C

From the question, P(x) = 0.084x - 1.5, R(x) = 0.21x.

Question a)

C = R(x) - P(x)

C = 0.21x - {0.084x - 1.5}

C = 0.21x - 0.084x + 1.5

C = 0.126x + 1.5

Question b)

If C = 0.126x + 1.5, then C at x = 7 units is gotten below as

C = 0.126(7) + 1.5

C = 0.882 + 1.5

C = 2.382.

Question c)

The break even point is the point where total revenue R(x) equals total cost C.

R(x) = 0.21x and C = 0.126x + 1.5

0.21x = 0.126x + 1.5

0.21x - 0.126x = 1.5

0.084x = 15

x = 15/ 0.084

x = 178.57 which is approximately 179 units (since quantity of units can't be decimal)