Question

2. Company manufactures and sells bikes. Each bike costs M R.O to make. The company's fixed costs are 500 R.O. In addition, the company owners know that the price of each bike comes from the price function p = 60 - (Note: M is the first two digit from your MEC ID after alphabetic (S or F), for example if the ID is 19F18140 take the two digit after F which are 18)

Answer 1

Cost function of Bike C (x) = 500+x

Price function P(x) = 60-0.5x

Revenue function = unit sold * Price = x * P(x) = x*(60-0.5x) =60x-0.5x^2

Break even point

C(x) = R(x)

500+x=60x-0.5x^2

0.5x^2-59x+500=0

So

x=108.81 =109

x=9.19036=9

P(109)= 60-0.5*109=5.5

P(9)= 60-0.5*9=55.5

So 9 bikes need to be sold for break-even

Answer b=Profit = R(x) - C(x) =60x-0.5x^2-500-x =-0.5x^2+59x-500

For profit maximization

dR(x)/dx=-x+59

x=59

So the profit maximinzatin is obtaied at 59 number of bikes

Answer c= maximim profit =-0.5*59*59+59*59-500 =1240.5