Question

Pearl’s Biking Company manufactures and sells bikes. Each bike costs £40 to make, and the company’s fixed costs are £5000. In addition, Pearl knows that the price of each bike comes from the price function P(x) = 300 – 2x where x is the total number of bikes manufactured and sold. Questions a) Find the company’s revenue function R(x), the company’s cost function C(x) and find the breakeven points

Answer 1

Answer:

R(x) = £[300 - 2x²]

C(x) = £[5000 + 40x]

The breakeven points are when number of bikes manufactured is 21 or 239

Step-by-step explanation:

The company price function P(x) = 300 - 2x. x is the number of items that can be sold at $P per item.

The revenue is given as price per item × number of item sold.

Revenue R(x) = xP(x) = x(300 - 2x) = 300x - 2x²

R(x) = £[300 - 2x²]

The cost function [C(x)] is the sum of variable cost and fixed cost. Therefore:

C(x) = fixed cost + variable cost

Since the fixed cost is £5000 and  Each bike costs £40, this means that the variable cost = 40 × number of items manufactured = 40 × x = 40x

Therefore C(x) = £[5000 + 40x]

At breakeven point, the cost of producing an item is equal to the revenue (amount the item is sold) gotten from the item.

That is cost = revenue,

C(x) = R(x)

5000 + 40x = 300x - x²

x² - 300x + 40x + 5000 = 0

x² - 260x + 5000 = 0

x ≈ 239  or x ≈ 21. The breakeven points are when number of bikes manufactured is 21 or 239