Answer:
R(x) =300·x - 2·x²
C(x) = £5000 + £40 × x
The break even points are 23.47 and 106.53 or 23 and 107 bikes
Explanation:
Given that the price function P(x) = 300 -2·x
Cost per bike = £40
The revenue function R(x) is given by bike price × total number of bikes manufactured and sold
∴ R(x) = P(x)×x = (300 - 2·x)×x = 300·x - 2·x²
The company's cost function, C(x) is Fixed cost + cost to produce each bike × total number of bikes produced
∴ C(x) = £5000 + £40 × x
The break even point is given by the relation;
Total revenue - total cost = 0
That is, break even point is R(x) - C(x) = 0
300·x - 2·x² - (5000 + 40·x) = 0
-2·x²+260·x-5000 = 0 or 2·x²- 260·x + 5000 = 0
Factorizing, we have;
(x - (65 -5√69))(x - (65 +5√69))
Solving gives x = 23.47 or 106.53
Therefore, the break even points are 23.47 and 106.53.
That is the company is profitable when they produce less than 23 bikes or more than 107 bikes.