Answer:
To address this problem, we can create a cost function for each production alternative that considers both fixed and variable costs. The total cost for each alternative is the sum of the fixed and variable costs. Let's denote:
�
Q as the number of chairs produced.
�
�
F
A
as the fixed cost for process A.
�
�
F
B
as the fixed cost for process B.
�
�
V
A
as the variable cost per unit for process A.
�
�
V
B
as the variable cost per unit for process B.
�
�
V
S
as the variable cost per unit from the outside supplier.
The total cost for each alternative is given by:
Process A:
�
�
(
�
)
=
�
�
+
�
�
⋅
�
C
A
(Q)=F
A
+V
A
⋅Q
Process B:
�
�
(
�
)
=
�
�
+
�
�
⋅
�
C
B
(Q)=F
B
+V
B
⋅Q
Outside Supplier:
�
�
(
�
)
=
�
�
⋅
�
C
S
(Q)=V
S
⋅Q
Now, let's address the specific questions:
a. Graphically plot the total costs for all three alternatives:
To graphically plot the total costs for all three alternatives, we can use the cost functions defined above. The x-axis will represent the quantity of chairs produced (
�
Q), and the y-axis will represent the total cost. The graph will have three lines, each representing one production alternative.
b. If the company produces only 600 chairs per year, which alternative is best?
Evaluate the total cost for each alternative when
�
=
600
Q=600 and compare them. The alternative with the lowest total cost at this production volume is the best choice.
c. If the company produces 3000 chairs per year, which alternative is best?
Similarly, evaluate the total cost for each alternative when
�
=
3000
Q=3000 and compare them. The alternative with the lowest total cost at this production volume is the best choice.
Additional Note:
When creating the graphical plot, it's important to identify the range of product volume where each alternative is the most cost-effective. This is typically done by examining the trends in the cost functions as the production volume increases.
To provide a more specific response, I would need the numerical values of
�
�
F
A
,
�
�
F
B
,
�
�
V
A
,
�
�
V
B
, and
�
�
V
S
. If you have those values, please provide them so that I can assist you further.
Explanation: