To determine the missing values [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] in the table, we can use the given data and formula. Here’s a step-by-step solution:
1. Given Data:
- Fixed monthly cost when no curtains are produced = \[tex]$1000.
- Costs for different numbers of curtains produced:
- 30 curtains: \$[/tex]4000
- 51 curtains: \[tex]$5335
- 56 curtains: \$[/tex]5760
- 70 curtains: \[tex]$6950
- C curtains: \$[/tex]7290
2. Step 1: Calculate Cost Per Curtain:
We need to find the average cost per curtain by using the given costs for different quantities.
- For 30 curtains:
[tex]\[
\text{Cost per curtain} = \frac{4000 - 1000}{30}
\][/tex]
- For 51 curtains:
[tex]\[
\text{Cost per curtain} = \frac{5335 - 1000}{51}
\][/tex]
- For 56 curtains:
[tex]\[
\text{Cost per curtain} = \frac{5760 - 1000}{56}
\][/tex]
- For 70 curtains:
[tex]\[
\text{Cost per curtain} = \frac{6950 - 1000}{70}
\][/tex]
Next, find the average cost per curtain:
[tex]\[
\text{Average cost per curtain} = \frac{\left(\frac{4000 - 1000}{30} + \frac{5335 - 1000}{51} + \frac{5760 - 1000}{56} + \frac{6950 - 1000}{70}\right)}{4}
\][/tex]
3. Step 2: Calculate Missing Values [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex]:
- For [tex]\(A\)[/tex] (Cost for 40 curtains):
[tex]\[
A = 1000 + (\text{Average cost per curtain} \times 40)
\][/tex]
- For [tex]\(B\)[/tex] (Cost for 60 curtains):
[tex]\[
B = 1000 + (\text{Average cost per curtain} \times 60)
\][/tex]
- For [tex]\(C\)[/tex] (Number of curtains produced when cost is \$7290):
[tex]\[
C = \frac{7290 - 1000}{\text{Average cost per curtain}}
\][/tex]
4. Final Values:
After doing the above calculations (which have been provided), we get the following values:
[tex]\[
A = 4550.0
\][/tex]
[tex]\[
B = 6325.0
\][/tex]
[tex]\[
C = 70.87 \approx 71 \; \text{(nearest whole number of curtains)}
\][/tex]
So, the missing values in the table are:
- [tex]\( A = 4550.0 \)[/tex]
- [tex]\( B = 6325.0 \)[/tex]
- [tex]\( C = 70.87 \approx 71 \)[/tex]
