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4. Marjorie manages a 200-seat, white-tablecloth restaurant in an upscale neighborhood. Since her guests expect her tablecloths and napkins to be really white, she sends her linens to a local laundry service daily. The laundry service charges her by the piece. She wants to keep track of her laundry cost per guest to see if she can use the information to control her laundry costs better. Help her complete her six-column cost per guest report. She has budgeted [tex]$\$[/tex]0.60[tex]$ per guest on average. How is she doing at controlling her laundry costs?

\begin{tabular}{|l|c|c|c|c|c|c|}
\hline
\multicolumn{6}{|l|}{Six-Column Cost per Guest - Laundry Service} \\
\hline
\multicolumn{4}{|l|}{Unit Name: Marjorie's} & \multicolumn{2}{|c|}{Number of Guests Served} & \multicolumn{2}{|c|}{Date: 5/1-5/7} \\
\hline
& Laundry Service Cost & \multicolumn{2}{|c|}{Cost per Guest} \\
\hline
Weekday & Today & To Date & Today & To Date & Today & To Date \\
\hline
1 & $[/tex]\[tex]$225$[/tex] & & 400 & & & \\
\hline
2 & [tex]$\$[/tex]204[tex]$ & & 375 & & & \\
\hline
3 & $[/tex]\[tex]$200$[/tex] & & 350 & & & \\
\hline
4 & [tex]$\$[/tex]240[tex]$ & & 425 & & & \\
\hline
5 & $[/tex]\[tex]$275$[/tex] & & 450 & & & \\
\hline
6 & [tex]$\$[/tex]300[tex]$ & & 500 & & & \\
\hline
7 & $[/tex]\[tex]$230$[/tex] & & 420 & & & \\
\hline
Total & & & & & & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let us break down the solution for calculating the laundry cost per guest for each day and cumulatively, and analyze Marjorie's performance against her budgeted cost per guest of \[tex]$0.60. We'll fill in the details of the six-column cost per guest report step-by-step. ### Given Information: - Laundry Service Costs for 7 days: \[225, 204, 200, 240, 275, 300, 230\] - Guests Served for 7 days: \[400, 375, 350, 425, 450, 500, 420\] - Budgeted Cost per Guest: \$[/tex]0.60

### Calculations:
1. Cost Per Guest (Today): This is calculated by dividing the laundry cost for each day by the number of guests served on that day.
2. Cost Per Guest (To Date): This is calculated by taking the cumulative total of the laundry costs up to that day and dividing it by the cumulative total number of guests served up to that day.

We'll go through the calculations for each day one by one.

### Day-by-Day Calculations:
Day 1:
- Laundry Service Cost = \[tex]$225 - Guests Served = 400 - Cost Per Guest (Today) = \(\frac{225}{400} = 0.5625\) Cumulative Calculations (To Date): - Total Laundry Cost (To Date) = \$[/tex]225
- Total Guests Served (To Date) = 400
- Cost Per Guest (To Date) = [tex]\(\frac{225}{400} = 0.5625\)[/tex]

---

Day 2:
- Laundry Service Cost = \[tex]$204 - Guests Served = 375 - Cost Per Guest (Today) = \(\frac{204}{375} = 0.544\) Cumulative Calculations (To Date): - Total Laundry Cost (To Date) = 225 + 204 = \$[/tex]429
- Total Guests Served (To Date) = 400 + 375 = 775
- Cost Per Guest (To Date) = [tex]\(\frac{429}{775} \approx 0.5535\)[/tex]

---

Day 3:
- Laundry Service Cost = \[tex]$200 - Guests Served = 350 - Cost Per Guest (Today) = \(\frac{200}{350} \approx 0.5714\) Cumulative Calculations (To Date): - Total Laundry Cost (To Date) = 429 + 200 = \$[/tex]629
- Total Guests Served (To Date) = 775 + 350 = 1125
- Cost Per Guest (To Date) = [tex]\(\frac{629}{1125} \approx 0.5591\)[/tex]

---

Day 4:
- Laundry Service Cost = \[tex]$240 - Guests Served = 425 - Cost Per Guest (Today) = \(\frac{240}{425} \approx 0.5647\) Cumulative Calculations (To Date): - Total Laundry Cost (To Date) = 629 + 240 = \$[/tex]869
- Total Guests Served (To Date) = 1125 + 425 = 1550
- Cost Per Guest (To Date) = [tex]\(\frac{869}{1550} \approx 0.5606\)[/tex]

---

Day 5:
- Laundry Service Cost = \[tex]$275 - Guests Served = 450 - Cost Per Guest (Today) = \(\frac{275}{450} \approx 0.6111\) Cumulative Calculations (To Date): - Total Laundry Cost (To Date) = 869 + 275 = \$[/tex]1144
- Total Guests Served (To Date) = 1550 + 450 = 2000
- Cost Per Guest (To Date) = [tex]\(\frac{1144}{2000} = 0.572\)[/tex]

---

Day 6:
- Laundry Service Cost = \[tex]$300 - Guests Served = 500 - Cost Per Guest (Today) = \(\frac{300}{500} = 0.6\) Cumulative Calculations (To Date): - Total Laundry Cost (To Date) = 1144 + 300 = \$[/tex]1444
- Total Guests Served (To Date) = 2000 + 500 = 2500
- Cost Per Guest (To Date) = [tex]\(\frac{1444}{2500} = 0.5776\)[/tex]

---

Day 7:
- Laundry Service Cost = \[tex]$230 - Guests Served = 420 - Cost Per Guest (Today) = \(\frac{230}{420} \approx 0.5476\) Cumulative Calculations (To Date): - Total Laundry Cost (To Date) = 1444 + 230 = \$[/tex]1674
- Total Guests Served (To Date) = 2500 + 420 = 2920
- Cost Per Guest (To Date) = [tex]\(\frac{1674}{2920} \approx 0.5733\)[/tex]

### Summary Table:
[tex]\[ \begin{array}{|l|c|c|c|c|c|c|} \hline \text{Weekday} & \text{Laundry Service Cost (Today)} & \text{Guests Served (Today)} & \text{Cost Per Guest (Today)} & \text{Total Laundry Cost (To Date)} & \text{Total Guests} & \text{Cost Per Guest (To Date)} \\ \hline \text{1} & \$225 & 400 & 0.5625 & 225 & 400 & 0.5625 \\ \hline \text{2} & 204 & 375 & 0.544 & 429 & 775 & 0.5535 \\ \hline \text{3} & 200 & 350 & 0.5714 & 629 & 1125 & 0.5591 \\ \hline \text{4} & 240 & 425 & 0.5647 & 869 & 1550 & 0.5606 \\ \hline \text{5} & 275 & 450 & 0.6111 & 1144 & 2000 & 0.572 \\ \hline \text{6} & 300 & 500 & 0.6 & 1444 & 2500 & 0.5776 \\ \hline \text{7} & 230 & 420 & 0.5476 & 1674 & 2920 & 0.5733 \\ \hline \text{Total} & & & & 1674 & 2920 & \\ \hline \end{array} \][/tex]

### Analysis:
- The overall cost per guest "to date" fluctuates around the budgeted amount of \[tex]$0.60. - Generally, Marjorie is doing well, but on some days the cost is higher than the budget (notably on day 5). - The cumulative cost per guest to date (0.5733) is below the budgeted amount of \$[/tex]0.60, indicating good control over laundry costs overall.

Marjorie appears to be managing her laundry costs effectively, but she should continue monitoring it closely to ensure individual days do not exceed the budgeted amount, thus maintaining the overall average.

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