You are curious as to how much Rhonda and Steve made in their business last year. You do not have all the data, but you know that most of their expenses relate to buying the sweaters and having them monogrammed. You know they paid themselves $\$50,000$ each and you know the rent, utilities, insurance, and a benefit package for the business was about $\$20,000$. About how much do you think they made “before taxes” last year? If they must make their payment to the venture capital firm, and then pay 50 percent in taxes, what was their increase in cash last year?

Palin’s Muffler Shop has one standard muffler that fits a large variety of cars. The shop wishes to establish a periodic review system to manage inventory of this standard muffler. Use the information in the following table to determine the optimal inventory target level (or order-up-to level). What is the optimal target level (order-up-to level)?

Sarah’s Muffler Shop has one standard muffler that fits a large variety of cars. Sarah wishes to establish a reorder point system to manage inventory of this standard muffler. Use the following information to determine the best order size and the reorder point.

It is your responsibility, as the new head of the automotive section of Nichols Department Store, to ensure that reorder quantities for the various items have been correctly established. You decide to test one item and choose Michelin tires, XW size $185 \times 14 \mathrm{BSW}$. A perpetual inventory system has been used, so you examine this, as well as other records, and come up with the following data.

$$\begin{array}{ll} \text { Cost per tire } & \$ 35 \text { each } \\ \text { Holding cost } & 20 \text { percent of tire cost per year } \\ \text { Demand } & 1,000 \text { per year } \\ \text { Ordering cost } & \$ 20 \text { per order } \\ \text { Standard deviation of daily demand } & 3 \text { tires } \\ \text { Delivery lead time } & 4 \text { days } \\ \hline \end{array}$$

Because customers generally do not wait for tires but go elsewhere, you decide on a service probability of $98$ percent. Assume the demand occurs $365$ days per year.

a. Determine the order quantity.

b. Determine the reorder point.

Your project to obtain charitable donations is now $30$ days into a planned $40$-day project. The project is divided into three activities. The first activity is designed to solicit individual donations. It is scheduled to run the first $25$ days of the project and to bring in $\$ 25,000$. Even though we are $30$ days into the project, we still see that we have only $90$ percent of this activity complete. The second activity relates to company donations and is scheduled to run for $30$ days starting on day $5$ and extending through day $35$ . We estimate that, even though we should have $83$ percent $(25 / 30)$ of this activity complete, it is actually only $50$ percent complete. This part of the project was scheduled to bring in $\$ 150,000$ in donations. The final activity is for matching funds. This activity is scheduled to run the last 10 days of the project and has not started. It is scheduled to bring in an additional $\$ 50,000$. So far, $\$ 175,000$ has actually been brought in on the project. Calculate the Schedule Variance, Schedule Performance Index, and Cost (actually value in this case) Performance Index. How is the project going? (Hint: Note that this problem is different since revenue rather than cost is the relevant measure. Use care in how the measures are interpreted.)

A fast-food restaurant serves hamburgers, cheeseburgers, and chicken sandwiches. The restaurant counts a cheeseburger as equivalent to $1.25$ hamburgers and chicken sandwiches as $0.8$ hamburger. Current employment is five full-time employees who each work a $40$-hour week. If the restaurant sold $700$ hamburgers, $900$ cheeseburgers, and $500$ chicken sandwiches in one week, what is its productivity? What would its productivity have been if it had sold the same number of sandwiches $(2,100)$, but the mix was $700$ of each type?

You are curious as to how much Rhonda and Steve made in their business last year. You do not have all the data, but you know that most of their expenses relate to buying the sweaters and having them monogrammed. You know they paid themselves $\$ 50,000$ each and you know the rent, utilities, insurance, and a benefit package for the business was about $\$ 20,000$. About how much do you think they made "before taxes" last year? If they must make their payment to the venture capital firm, and then pay $50$ percent in taxes, what was their increase in cash last year?

One unit of A is made of two units of B and one unit of C. B is made of three units of D and one unit of F. C is composed of three units of B, one unit of D, and four units of E. D is made of one unit of E. Item C has a lead time of one week; items A, B, E, and F have two-week lead times; and item D has a lead time of three weeks. Lot-for-lot (L4L) lot sizing is used for items C, E, and F; lots of size 20, 40, and 160 are used for items A, B, and D, respectively. Items A, B, D, and E have on-hand (beginning) inventories of 5, 10, 100, and 100, respectively; all other items have zero beginning inventories. We are scheduled to receive 10 units of A in week 3, 20 units of B in week 7, 40 units of F in week 5, and 60 units of E in week 2; there are no other scheduled receipts. If 20 units of A are required in week 10, use the low-level-coded bill-of-materials (product structure tree) to find the necessary planned order releases for all components.

The model most appropriate for making a one-time purchase of an item

A particular forecasting model was used to forecast a six-month period. Here are the forecasts and actual demands that resulted. Find the tracking signal and state whether you think the model being used is giving acceptable answers.

Demand for stereo headphones and MP$3$ players for joggers has caused Nina Industries to grow almost $50$ percent over the past year. The number of joggers continues to expand, so Nina expects demand for headsets to also expand, because, as yet, no safety laws have been passed to prevent joggers from wearing them. Demand for the players for last year was as follows.

$$\begin{array}{lc} \text { Month } & \begin{array}{c} \text { Demand } \\ \text { (units) } \end{array} \\ \hline \text { January } & 4,200 \\ \text { February } & 4,300 \\ \text { March } & 4,000 \\ \text { April } & 4,400 \\ \text { May } & 5,000 \\ \text { June } & 4,700 \\ \hline \end{array} \begin{array}{ll} &\text { Demand }\\ \text { Month } & \text { (units) } \\ \hline \text { July } & 5,300 \\ \text { August } & 4,900 \\ \text { September } & 5,400 \\ \text { October } & 5,700 \\ \text { November } & 6,300 \\ \text { December } & 6,000 \\ \hline \end{array}$$

a. Using linear regression analysis, what would you estimate demand to be for each month next year? Using a spreadsheet, follow the general format in Exhibits $18.7$ and $18.8$. Compare your results to those obtained by using the forecast spreadsheet function.

b. To be reasonably confident of meeting demand, Nina decides to use three standard errors of estimate for safety. How many additional units should be held to meet this level of confidence?

What is the term used to refer to inventory while in distribution—that is, being moved within the supply chain?

Consumer Reports, the service that reports unbiased testing and ratings on cars (together with about everything else we buy), recommends avoiding new cars in their first year of production, especially those loaded with new technology. What can Tesla do to refute this recommendation?

Starbucks is considering simplifying the supply chain for their coffeemaker. Instead of stocking the coffeemaker in all five distribution centers, they are considering only supplying it from a single location. Evaluate this option by analyzing how accurate the forecast would be based on the demand aggregated across all regions. Use the model that you think is best from your analysis of the previous questions. Evaluate your new forecast using mean absolute deviation, mean absolute percent error, and the tracking signal.