Answer:
1. Fixed cost is $800
2.Cost of 25 bags is $1025
3. (170,2300)
Step-by-step explanation:
Given
[tex]c(x) = 10x + 800[/tex]
Solving (a): Fixed cost
From the question, fixed cost is when x = 0;
Substitute 0 for x in [tex]c(x) = 10x + 800[/tex]
[tex]c(0) = 10 * 0 + 800[/tex]
[tex]c(0) = 0 + 800[/tex]
[tex]c(0) = 800[/tex]
Hence, the fixed cost is $800
Solving (b): Cost of making 25 items
Here; x = 25
Substitute 25 for x in [tex]c(x) = 10x + 800[/tex]
[tex]c(25) = 10 * 25 + 800[/tex]
[tex]c(25) = 250 + 800[/tex]
[tex]c(25) = 1025[/tex]
Hence, the cost of 25 bags is $1025
Solving (c): Domain and Range where Maximum cost = $2300
Here; c(x) = 2500
Substitute 25 for c(x) in [tex]c(x) = 10x + 800[/tex]
[tex]2500 = 10x + 800[/tex]
Subtract 800 from both sides
[tex]10x = 2500 - 800[/tex]
[tex]10x = 1700[/tex]
Divide both sides by 10
[tex]x = 170[/tex]
The domain and range of a function is in form of (x,c(x))
Hence, the domain and range is (170,2300)