To determine the manufacturing cost per scissors, we need to add the material cost and the labor cost, then find the cost per unit by considering how these costs distribute across the number of scissors produced.
First, let's state the given functions:
1. Material cost function: [tex]\( M(s) = 225 + 0.65s \)[/tex]
2. Labor cost function: [tex]\( L(s) = 54 + 1.15s \)[/tex]
Next, we combine these to find the total manufacturing cost, [tex]\( C(s) \)[/tex]:
[tex]\[ C(s) = M(s) + L(s) = (225 + 0.65s) + (54 + 1.15s) \][/tex]
Combining the terms, we get:
[tex]\[ C(s) = 225 + 54 + 0.65s + 1.15s \][/tex]
[tex]\[ C(s) = 279 + 1.8s \][/tex]
This is the total manufacturing cost for producing [tex]\( s \)[/tex] scissors.
To find the manufacturing cost per scissors, we need to divide the total cost by [tex]\( s \)[/tex]:
[tex]\[ \text{Cost per scissors} = \frac{C(s)}{s} = \frac{279 + 1.8s}{s} \][/tex]
Thus, the correct expressions for the manufacturing cost and the manufacturing cost per scissors are:
1. Total manufacturing cost: [tex]\( 279 + 1.8s \)[/tex]
2. Manufacturing cost per scissors: [tex]\(\frac{279 + 1.8s}{s}\)[/tex]
So, from the given options:
A. [tex]\(171 - 0.50s\)[/tex] is incorrect.
B. [tex]\(279 + 1.80s\)[/tex] is the correct expression for the total manufacturing cost.
C. [tex]\(\frac{279 + 1.80 \text{s}}{s}\)[/tex] is the correct expression for the manufacturing cost per scissors.
D. [tex]\(\frac{171 - 0.50s}{s}\)[/tex] is incorrect.
The correct expressions are:
- Total manufacturing cost: [tex]\( 279 + 1.8s \)[/tex] (corresponding to option B)
- Manufacturing cost per scissors: [tex]\(\frac{279 + 1.8s}{s}\)[/tex] (corresponding to option C)
Therefore, the correct answer is:
C. [tex]\(\frac{279 + 1.80 \text {s}}{s}\)[/tex]
