The cost in dollars of making x items is given by the function C(x)=10x+600. (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 15 items? (c) Suppose the maximum cost allows is $1600. What are the domain and range of the cost function, C(x)? (Enter your answers using interval notation.)

The fixed cost for the item is $600, the cost of making 15 items is $750, and the domain and range of the cost function, C(x) are (100,1600) and this can be determined by using the arithmetic operations.

Given :

The cost in dollars of making x items is given by the function (C(x) = 10x + 600)

A). Given that zero items are produced that means the value of (x = 0). Put the value of x in the given function.

C(x) = 10x + 600

C(0) = 0 + 600

C(0) = $600

So, the fixed cost for this item is $600.

B). The cost of making 15 items means that (x = 15). Put the value of x in the given function.

C(x) = 10x + 600

C(15) = 10(15) + 600

C(15) = $750

So, the cost of making 15 items is $750.

C). Given that the maximum cost allows is $1600 that means C(x) = 1600. Put the value of C(x) in the given function.

1600 = 10x + 600

1000 = 10x

100 = x

Therefore, the domain and range of the cost function, C(x) are (100,1600).

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- Fixed cost is 600

- The cost of making 15 items is 600

- The cost function is (100,1600)

Step-by-step explanation:

Given

Calculating (a) Fixed Cost

Fixed cost is when x = 0

Substitute 0 for x

Hence, the fixed cost is 600

Calculating (b) Cost of 15 items

Here, x = 15

Substitute 15 for x

Hence, the cost of making 15 items is 600

Calculating (c) Domain and Range

Here, C(x) = 1600

Substitute 1600 for C(x)

Make x the subject of formula

Hence, the cost function is (100,1600)

were is the equation