he cost in dollars of making x items is given by the function C(x) = 10x + 500.

a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item.

b. What is the cost of making 25 items?

c. Suppose the maximum cost allowed is $1500. What are the domain and range of the cost function, C(x)?

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varshamittal029 varshamittal029 · Answer 1 · 2022-09-13T07:50:46+02:00

We get the fixed cost as $ 150, cost of 25 items as $ 750, range as [0, 1500] and the domain as [0,150].

We are given the cost function:

C(x) = 10x + 500.

Fixed cost is when x = 0

C(0) = Fixed cost = 10 ( 0 ) + 500

Fixed cost = $ 500

Cost of making 25 products is x = 25

C(25) = 10 (25) + 500

C(25) = 250 + 500 = $ 750

Maximum cost allowed = $ 1500

Function becomes:

10x + 500 ≤ 1500

x + 50 ≤ 150

x ≤ 150 - 50

x ≤ 100

Range = [0, 1500]

Domain = [0, 150]

Therefore, we get the fixed cost as $ 150, cost of 25 items as $ 750, range as [0, 1500] and the domain as [0,150].

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