Question

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.)

Answer 1

Answer:

- Fixed cost is 600

- The cost of making 15 items is 600

- The cost function is (100,1600)

Step-by-step explanation:

Given

$C(x) = 10x + 600$

Calculating (a) Fixed Cost

Fixed cost is when x = 0

Substitute 0 for x

$C(0) = 10 * 0 + 600$

$C(0) = 0 + 600$

$C(0) = 600$

Hence, the fixed cost is 600

Calculating (b) Cost of 15 items

Here, x = 15

Substitute 15 for x

$C(15) = 10 * 15 + 600$

$C(15) = 150 + 600$

$C(15) = 750$

Hence, the cost of making 15 items is 600

Calculating (c) Domain and Range

Here, C(x) = 1600

Substitute 1600 for C(x)

$1600 = 10x + 600$

Make x the subject of formula

$1600 - 600 = 10x$

$1000 = 10x$

$x = 100$

Hence, the cost function is (100,1600)