Question

"The start-up cost of a company is $150.000. Itcosts $.17 to manufacture each beadset. Graphthe function that represents the average cost of aheadsel. How many must be manufactured to resultin a cost of less than $5 per headset?

Answer 1

Let x the number of headsets produced

f(x) the total cost for producing x headsets

f(x) = 150000 + 0.17x

the average cost of headset c(x) is

c(x) = f(x)/x

that is:

c(x) = 150,000/x + 0.17

the graph of this function is:

now, we need to find x such that c(x) < 5, that is:

150000/x + 0.17 < 5

by solving we find

x > 31,055 headsets

we can conclude that the correct answer is:

and

x > 31,055 headsets