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
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