Math, asked by Umapathi6426, 8 months ago

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. b) By plotting the revenue and cost functions, obtain the Break-even output levels and corresponding price (use graph paper or graphical tools). c) Generate the profit function for the company and find, i. The level production that maximizes the profit. ii. The maximum profit.

Answers

Answered by amitnrw
0

Given :  Pearl’s Biking Company manufactures and sells bikes. Each bike costs £40 to make, and the company’s fixed costs are £5000.   price function P(x) = 300 – 2x where x is the total number of bikes manufactured and sold.

To find : company’s revenue function R(x)  the company’s cost function  Break-even   , profit function

Solution:

Cost function of Bike

C (x)  =  5000 + 40x

Price

P(x)  =  300 – 2x

Revenue function  = unit sold * Price  = x * P(x)

R ((x) =  x (300 - 2x) = 300x - 2x²

Break even point  

C(x)  =  R(x)

=> 5000 + 40x =  300x - 2x²

=> 2x² - 260x  + 5000 = 0

=> x² - 130x  + 2500 = 0

=> x  =  23.5  = 24     or  106.5 = 106

24 bikes need to be sold for break even

P(24) = 300 -2(24)  = 252 £

P(106) = 300 -2(106)  = 88 £

Profit =  R(x) - C(x) =  300x - 2x² -  5000 - 40x

P(x) =   - 2x²  + 260x  - 5000

dP/dx =  - 4x  + 260

=> x = 65

d²P/dx² = - 4

Selling 65 bike will give maximum profit

Maximum profit =  - 2x²  + 260x  - 5000   = 3450 £

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