Question

Question: A manufacturer keeps track of his monthly costs by using a “cost function” that assigns a total cost for a given number of manufactured items, x. The function is C(x) = 7,500 + 2.4x a) What is the reasonable domain of the function? b) What is the cost of 3,500 items? c) If costs must be kept below $20,000 this month, what is the greatest number of items she can manufacture? You must show your work

Answer 1

a) Domain: -∞ < x < ∞

b) Cost required to manufacture 3500 items is $15,900.

c) Number of items she can manufacture is 5208 if cost is kept at $20,000

Explanation:

a) What is the reasonable domain of the function?

The function is C(x) = 7,500 + 2.4x

The domain of the function is the set of values for which the function is defined and valid.

In the given function there is no constraint or undefined points so domain is:

-∞ < x < ∞

b) What is the cost of 3,500 items?

We are given x = 3500 and we need to find the cost.

Putting values in the function given:

C(x) = 7,500 + 2.4x

C(x) = 7,500 + 2.4 (3500)

C(x) = 7500 + 8400

C(x) = 15,900

Cost required to manufacture 3500 items is $15,900.

c) If costs must be kept below $20,000 this month, what is the greatest number of items she can manufacture?

We are given cost, and we need to find x

C(x) = 7,500 + 2.4x

20,000 = 7500 +2.4x

20,000 - 7500 = 2.4x

12500 = 2.4 x

=> x = 12500/2.4

x= 5208.3 ≅ 5208

So, Number of items she can manufacture is 5208 if cost is kept at $20,000