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The cost in dollars of making x items is given by the function C(x)= 10x+600A.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 $1600 What are the domain and range of the cost function,C(x)



Answer :

Step 1

Given;

[tex]\begin{gathered} C(x)=10x+600 \\ x=number\text{ of items} \end{gathered}[/tex]

Step 2

The fixed cost is determined when zero items are produced. Therefore, the fixed cost will be;

[tex]C(x)=10(0)+600=\text{ \$}600[/tex]

Step 3

Find the cost of making 25 items

[tex]C(25)=10(25)+600=250+600=\text{ \$}850[/tex]

Step 4

Suppose the maximum cost allowed is $1600

[tex]\begin{gathered} C(x)=1600 \\ 1600=10x+600 \\ 1600-600=10x \\ 1000=10x \\ x=100\text{ items} \end{gathered}[/tex]

The domain and range of the cost function when will be;

[tex]\begin{gathered} Domain=[0,100] \\ Range=[600,1600] \end{gathered}[/tex]

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