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.

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ChiKesselman ChiKesselman · Answer 1 · 2019-12-05T08:08:15+01:00

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:

[tex]C(x) = 50x + 5000[/tex]

Average daily cost is given by:

[tex]\displaystyle\frac{50x+5000}{x}[/tex]

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:

[tex]\displaystyle\frac{50x+5000}{x} \leq 150\\\\50x + 5000 \leq 150x\\150x-50x \geq 5000\\100x \geq 5000\\x \geq 50[/tex]

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