Respuesta :
Answer:
- Fixed cost is 600
- The cost of making 15 items is 600
- The cost function is (100,1600)
Step-by-step explanation:
Given
[tex]C(x) = 10x + 600[/tex]
Calculating (a) Fixed Cost
Fixed cost is when x = 0
Substitute 0 for x
[tex]C(0) = 10 * 0 + 600[/tex]
[tex]C(0) = 0 + 600[/tex]
[tex]C(0) = 600[/tex]
Hence, the fixed cost is 600
Calculating (b) Cost of 15 items
Here, x = 15
Substitute 15 for x
[tex]C(15) = 10 * 15 + 600[/tex]
[tex]C(15) = 150 + 600[/tex]
[tex]C(15) = 750[/tex]
Hence, the cost of making 15 items is 600
Calculating (c) Domain and Range
Here, C(x) = 1600
Substitute 1600 for C(x)
[tex]1600 = 10x + 600[/tex]
Make x the subject of formula
[tex]1600 - 600 = 10x[/tex]
[tex]1000 = 10x[/tex]
[tex]x = 100[/tex]
Hence, the cost function is (100,1600)
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).
For more information, refer to the link given below:
https://brainly.com/question/13101306
