How many bicycles must be produced each day in order for the average cost to be no more than $130?

Question

Suppose the daily cost C of manufacturing x bicycles is given by C(x)=90x+4600. Now the average daily cost is given by C(x)=90x+4600/x. How many bicycles must be produced each day in order for the average cost to be no more than $130?

a)either 115 or more bicycles or 0 or fewer bicycles must be produced

b)115 or fewer bicycles must be produced

c)115 or more bicycles must be produced

d)between 0 and 115 bicycles must be produced

Answer 1

c) looks correct, or better than a,b, and d, without doing any calculations other than noticing if x=0, average cost is infinite

Total C(x) = 90x +4600

Average C(x) = (90x+4600)/x = 90+4600/x= 130

4600/x = 130-90 = 40

x = 4600/40 = 115 minimum to keep average cost under 130