Jeffrey Helm owns a health and fitness center called Bulk-Up in Harrisburg. He is considering adding more floor space to meet increasing demand. He will either add no floor space $(\mathrm{N})$, a moderate area of floor space $(\mathrm{M})$, a large area of floor space (L), or an area of floor space that doubles the size of the facility (D). Demand will either stay fixed, increase slightly, or increase greatly. The following are the changes in Bulk-Up's annual profits under each combination of expansion level and demand change level:

	EXPANSION LEVEL
DEMAND CHANGE	N	M	L	D
Fixed	$\$0$	$-\$4,000$	$-\$10,000$	$-\$50,000$
Slight increase	$\$2,000$	$\$8,000$	$\$6,000$	$\$4,000$
Major increase	$\$3,000$	$\$9,000$	$\$20,000$	$\$40,000$

Jeffrey is risk averse and wishes to use the maximin criterion.

What are his decision alternatives and what are the states of nature?

The University of Miami bookstore stocks textbooks in preparation for sales each semester. It normally relies on departmental forecasts and preregistration records to determine how many copies of a text are needed. Preregistration shows 90 operations management students enrolled, but bookstore manager Vaidy Jayaraman has second thoughts, based on his intuition and some historical evidence. Vaidy believes that the distribution of sales may range from 70 to 90 units, according to the following probability model:

This textbook costs the bookstore $\$ 82$ and sells for $\$ 112$. Any unsold copies can be returned to the publisher, less a restocking fee and shipping, for a net refund of $\$ 36$.

How many copies should the bookstore stock to achieve highest expected value?

Use the simplex method to solve each linear programming problem. Maximize

$$z=8x_{1}+10x_{2}+7x_{3}$$

subject to:

$$\left[\begin{array}{llll} x_{1} & +3x_{2} & +2x_{3} & \leq 10\\ x_{1} & +5x_{2} & +x_{3} & \leq 8 \end{array}\right]$$

with

$$x_{1}\geq 0,\ x_{2}\geq 0,\ x_{3}\geq 0$$

The city of Belgrade, Serbia, is contemplating building a second airport to relieve congestion at the main airport and is considering two potential sites, $\mathrm{X}$ and $\mathrm{Y}$. Hard Rock Hotels would like to purchase land to build a hotel at the new airport. The value of land has been rising in anticipation and is expected to skyrocket once the city decides between sites $\mathrm{X}$ and $\mathrm{Y}$. Consequently, Hard Rock would like to purchase land now. Hard Rock will sell the land if the city chooses not to locate the airport nearby. Hard Rock has four choices: (1) buy land at X, (2) buy land at Y. (3) buy land at both $\mathrm{X}$ and $\mathrm{Y}$, or (4) do nothing. Hard Rock has collected the following data (which are in millions of euros):

*The second row of the table represents net operating profits from the hotel, not including the upfront cost of land.

Hard Rock determines there is a $45 \%$ chance the airport will be built at $\mathrm{X}$ (hence, a $55 \%$ chance it will be built at $\mathrm{Y}$ ).

What should Hard Rock decide to do to maximize total net profit?

Jean-Marie Bourjolly's restaurant has the following inventory items that it orders on a weekly basis:

Which are C items?

Given the preceding product structure, master production schedule, and inventory status (Figure 14.12), develop a net materials requirements (planned order release) for all items.

You are expected to have the gift bags in Problem $14.1$ ready at 5 P.M. However, you need to personalize the items (monogrammed pens, note pads, literature from the printer, etc.). The lead time is 1 hour to assemble $200 \mathrm{Js}$ once the other items are prepared. The other items will take a while as well. Given the volunteers you have, the other time estimates are item $\mathrm{K}$ ( 2 hours), item L ( 1 hour), and item M (4 hours). Develop a time-phased assembly plan to prepare the gift bags.

Five-year-old Cheyenne Stark was riding in the backseat of her parents’ Ford Taurus. Cheyenne was not sitting in a booster seat. Instead, she was using a seatbelt designed by Ford, but was wearing the shoulder belt behind her back. The car was involved in a collision. As a result, Cheyenne suffered a spinal cord injury and was paralyzed from the waist down. The family filed a suit against Ford Motor Co., alleging that the seatbelt was defectively designed. Could Ford successfully claim that Cheyenne had misused the seatbelt? Why or why not? [Stark v. Ford Motor Co., 365 N.C. 468, 723 S.E.2d 753 (2012)] (See Defenses to Product Liability.)

Phillip Witt, president of Witt Input Devices, wishes to create a portfolio of local suppliers for his new line of keyboards. As the suppliers all reside in a location prone to hurricanes, tornadoes, flooding, and earthquakes, Phillip believes that the probability in any year of a "super-event" that might shut down all suppliers at the same time for at least 2 weeks is 3%. Such a total shutdown would cost the company approximately $400,000. He estimates the "unique-event" risk for any of the suppliers to be 5%. Assuming that the marginal cost of managing an additional supplier is$15,000 per year, how many suppliers should Witt Input Devices use? Assume that up to three nearly identical local suppliers are available.

The IRS has determined that during each of the next 12 months it will need the number of supercomputers given in Table 45. To meet these requirements, the IRS rents supercomputers for a period of one, two, or three months. It costs $100 to rent a supercomputer for one month,$180 for two months, and $250 for three months. At the beginning of month 1, the IRS has no supercomputers. Determine the rental plan that meets the next 12 months’ requirements at minimum cost. Note: You may assume that fractional rentals are okay, so if your solution says to rent 140.6 computers for one month we can round this up or down (to 141 or 140) without having much effect on the total cost. Table 45:

$$\begin{matrix} \text{Month} & \text{Computer Requirements}\\ \text{1} & \text{800}\\ \text{2} & \text{1,000}\\ \text{3} & \text{600}\\ \text{4} & \text{500}\\ \text{5} & \text{1,200}\\ \text{6} & \text{400}\\ \text{7} & \text{800}\\ \text{8} & \text{600}\\ \text{9} & \text{400}\\ \text{10} & \text{500}\\ \text{11} & \text{800}\\ \text{12} & \text{600}\\ \end{matrix}$$

Each hour from 10 a.m. to 7 p.m., Bank One receives checks and must process them. Its goal is to process all the checks the same day they are received The bank has 13 check-processing machines, each of which can process up to 500 checks per hour. It takes one worker to operate each machine. Bank One hires both full-time and part-time workers. Full-time workers work 10 a.m.–6 p.m., 11 a.m.– 7 p.m., or Noon–8 p.m. and are paid $160 per day. Part-time workers work either 2 p.m.–7 p.m. or 3 p.m.– 8 p.m. and are paid$75 per day. The number of checks received each hour is given in Table 6. In the interest of maintaining continuity. Bank One believes it must have at least three full-time workers under contract. Develop a cost-minimizing work schedule that processes all checks by 8 p.m. TABLE 6:

$$\begin{matrix} \text{Time} & \text{Checks Received}\\ \text{10 a.m.} & \text{5,000}\\ \text{11 a.m.} & \text{4,000}\\ \text{Noon} & \text{3,000}\\ \text{1 p.m.} & \text{4,000}\\ \text{2 p.m.} & \text{2,500}\\ \text{3 p.m.} & \text{3,000}\\ \text{4 p.m.} & \text{4,000}\\ \text{5 p.m.} & \text{4,500}\\ \text{6 p.m.} & \text{3,500}\\ \text{7 p.m.} & \text{3,000}\\ \end{matrix}$$

Par, Inc., produces a standard golf bag and a deluxe golf bag on a weekly basis. Each golf bag requires time for cutting and dyeing and time for sewing and finishing, as shown in the following table:

The profits per bag and weekly hours available for cutting and dyeing and for sewing and finishing are as follows:

Par, Inc., will sell whatever quantities it produces of these two products.

What is the value of the profit?

A manager must decide which type of machine to buy, A, B, or C. Machine costs are as follows:

Product forecasts and processing times on the machines are as follows

a. Assume that only purchasing costs are being considered. Which machine would have the lowest total cost, and how many of that machine would be needed? Machines operate 10 hours a day, 250 days a year.

b. Consider this additional information: The machines differ in terms of hourly operating costs: The A machines have an hourly operating cost of$10 each, B machines have an hourly operating cost of $11 each, and C machines have an hourly operating cost of$12 each. Which alternative would be selected, and how many machines, in order to minimize total cost while satisfying capacity processing requirements

A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed. What percentage of time is the urn being used?