Answer:
R(x) = £[300 - 2x²]
C(x) = £[5000 + 40x]
The breakeven points are when number of bikes manufactured is 21 or 239
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