Question

Suppose the daily cost C of manufacturing x bicycles is given by C(x) = 50x + 5000. Now the average daily cost is given by C(x) = 50x + 5000/x. How many bicycles must be produced each day in order for the average cost to be no more than $150? Choose the correct answer below. 50 or more bicycles must be produced. 50 or fewer bicycles must be produced. Either 50 or more bicycles or 0 or fewer bicycles must be produced. Between 0 and 50 bicycles must be produced.

Answer 1

Answer:

Option A) 50 or more bicycles must be produced.

Step-by-step explanation:

We are given the following information in the question:

Cost of manufacturing x bicycles is given by:

$C(x) = 50x + 5000$

Average daily cost is given by:

$\displaystyle\frac{50x+5000}{x}$

We have to find the number of bicycles that must be produced each day in order for the average cost to be no more than $150

Thus, we can write:

$\displaystyle\frac{50x+5000}{x} \leq 150\\\\50x + 5000 \leq 150x\\150x-50x \geq 5000\\100x \geq 5000\\x \geq 50$

So, in order for the average cost to be no more than $150, 50 or more bicycles must be produced.