Question

The cost in dollars of making x items is given by the function C(x)=10x+900 .

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



Fixed cost =$



b. What is the cost of making 25 items?



C(25)=$



c. Suppose the maximum cost allowed is $1900 . What are the domain and range of the cost function, C(x) ?

Domain:
Range:

Answer 1

Explanation:

when we give a function an actual value as argument, we are using the variable(s) in the functional definition as intended : as placeholders for actual values.

so, we only need to replace any occurrence of the variable by the actual value and calculate.

a.

zero items are produced means x = 0.

C(0) = 10×0 + 900 = $900

fixed cost = $900

b.

making 25 items means x = 25.

C(25) = 10×25 + 900 = 250 + 900 = $1,150

c.

the domain is the interval or set of all valid values for x.

the range is the interval or set of all valid values for y (the functional result).

now, the maximum cost allowed is $1900.

how many items are that ?

1900 = 10x + 900

1000 = 10x

x = 100

so, the domain is

0 <= x <= 100

the range is

$900 <= y <= $1900