Question

The cost in dollars of making x items is given by the function C(x)=10x+800. 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 $3300. What are the domain and range of the cost function, C(x)? (In interval Notation)

im struggling with C terribly i Just dont understand it


When you enter a number in your answer, do not enter any commas in that number. In other words if you want to enter one thousand, then type in 1000 and not 1,000. It's not possible to understand what the interval (1,000,2,000) means, so you should write that as (1000,2000).

Answer 1

9514 1404 393

Answer:

a) $800

b) $1050

c) D: [0, 250]; R: [800, 3300]

Explanation:

a) The problem statement tells you the fixed cost is ...

C(0) = 800 . . . . dollars

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b) The cost of making 25 items is ...

C(25) = 10·25 +800 = 250 +800 = 1050 . . . . dollars

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c) You cannot make fewer than 0 items. The limit on cost means the most you can make is ...

3300 = 10x + 800

2500 = 10x

250 = x . . . . . . . . maximum number of items that can be made

So, the domain of the function -- the values of x to which it pertains -- is ...

0 ≤ x ≤ 250

In interval notation, this is [0, 250] . . . domain of C(x).

The range of C(x) is the set of cost values the function may have. We already know the minimum is 800. The problem statement tells us the maximum is 3300. The cost may have any value between those limits, so ...

800 ≤ C(x) ≤ 3300

In interval notation, this is [800, 3300] . . . range of C(x).

_____

Additional comment

Square brackets are used in interval notation when the "or equal to" case is part of the limit.

We could be more specific regarding domain and range, since the domain values are integers only, and the range values are multiples of 10 only. Here, we ignore that little detail.