Question

The revenue​ (in millions of​ dollars) from the sale of x units at a home supply outlet is given by ​R(x)equals=0.210.21x. The profit​ (in millions of​ dollars) from the sale of x units is given by ​P(x)equals=0.0860.086xminus−1.11.1. Find the cost equation. What is the​ break-even point?

Answer 1

Answer: a) c(x) = 0.124x + 1.1, b) 13 units

Step-by-step explanation: Revenue function = R(x) = 0.21x

Profit function = p(x) = 0.086 - 1.1

Cost function = c(x) =?

A)

Recall that profit = total revenue - total cost

Hence, total cost = total revenue - profit

c(x) = 0.21x - (0.086x - 1.1)

c(x) = 0.21x - 0.086x + 1.1

c(x) = 0.124x + 1.1

B)

Break even point is the point where total revenue equals total cost

R(x) = c(x)

0.21x = 0.124x + 1.1

0.21x - 0.124x = 1.1

0.086x = 1.1

x = 1.1/0.086

x = 12.79 which is approximately 13 units