Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Type I (Mountain View) Room Type II (Street View) Rental Class Super Saver Deluxe Business $40 $35 $35 $25 $45 Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 150 rentals in the Super Saver class, 55 in the Deluxe class, and 40 in the Business class. Since these are the forecasted demands, Round Tree will take no more than these amounts of each reservation for each rental class. Round Tree has a limited number of each type of room. There are 100 Type I rooms and 110 Type rooms. Deluxe (a) Formulate and solve a linear program to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. If an amount is zero, enter "0". Rental Class with room type No. of Reservations Super Saver rentals allocated to room type I Super Saver rentals allocated to room type II Deluxe rentals allocated to room type I Deluxe rentals allocated to room type II Business rentals allocated to room type II Business 95 65 50 95 X 0 5 (b) For the solution in part (a), how many reservations can be accommodated in each rental class? Rental Class No. of Reservations Super Saver 60 50 X * X

Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?

Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?

Scenario 3 Ben Gibson, the purchasing manager at Coastal Products, was reviewing purchasing expenditures for packaging materials with Jeff Joyner. Ben was particularly disturbed about the amount spent on corrugated boxes purchased from Southeastern Corrugated. Ben said, I dont like the salesman from that company. He comes around here acting like he owns the place. He loves to tell us about his fancy car, house, and vacations. It seems to me he must be making too much money off of us! Jeff responded that he heard Southeastern Corrugated was going to ask for a price increase to cover the rising costs of raw material paper stock. Jeff further stated that Southeastern would probably ask for more than what was justified simply from rising paper stock costs. After the meeting, Ben decided he had heard enough. After all, he prided himself on being a results-oriented manager. There was no way he was going to allow that salesman to keep taking advantage of Coastal Products. Ben called Jeff and told him it was time to rebid the corrugated contract before Southeastern came in with a price increase request. Who did Jeff know that might be interested in the business? Jeff replied he had several companies in mind to include in the bidding process. These companies would surely come in at a lower price, partly because they used lower-grade boxes that would probably work well enough in Coastal Products process. Jeff also explained that these suppliers were not serious contenders for the business. Their purpose was to create competition with the bids. Ben told Jeff to make sure that Southeastern was well aware that these new suppliers were bidding on the contract. He also said to make sure the suppliers knew that price was going to be the determining factor in this quote, because he considered corrugated boxes to be a standard industry item. Is Ben Gibson acting legally? Is he acting ethically? Why or why not?

Scenario 3 Ben Gibson, the purchasing manager at Coastal Products, was reviewing purchasing expenditures for packaging materials with Jeff Joyner. Ben was particularly disturbed about the amount spent on corrugated boxes purchased from Southeastern Corrugated. Ben said, I dont like the salesman from that company. He comes around here acting like he owns the place. He loves to tell us about his fancy car, house, and vacations. It seems to me he must be making too much money off of us! Jeff responded that he heard Southeastern Corrugated was going to ask for a price increase to cover the rising costs of raw material paper stock. Jeff further stated that Southeastern would probably ask for more than what was justified simply from rising paper stock costs. After the meeting, Ben decided he had heard enough. After all, he prided himself on being a results-oriented manager. There was no way he was going to allow that salesman to keep taking advantage of Coastal Products. Ben called Jeff and told him it was time to rebid the corrugated contract before Southeastern came in with a price increase request. Who did Jeff know that might be interested in the business? Jeff replied he had several companies in mind to include in the bidding process. These companies would surely come in at a lower price, partly because they used lower-grade boxes that would probably work well enough in Coastal Products process. Jeff also explained that these suppliers were not serious contenders for the business. Their purpose was to create competition with the bids. Ben told Jeff to make sure that Southeastern was well aware that these new suppliers were bidding on the contract. He also said to make sure the suppliers knew that price was going to be the determining factor in this quote, because he considered corrugated boxes to be a standard industry item. As the Marketing Manager for Southeastern Corrugated, what would you do upon receiving the request for quotation from Coastal Products?

At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.

In the​ past, Peter​ Kelle's tire dealership in Baton Rouge sold an average of 1,000 radials each year. In the past 2​ years, 240 and 240​, respectively were sold in​ fall, 350 and 320 in​ winter,150 and165 in​ spring, and 340 and 195 in summer. With a major expansion​ planned, Kelle projects sales next year to increase to 1,200 radials. Based on next​ year's projected​ sales, the demand for each season is going to be ​(enter your responses as whole​ numbers): Fall: Winter: Spring: Summer:

Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows:       Rental  Class         Super Saver Deluxe Business Room   Type I $30 $35 —     Type II $20 $30  $40 Type I rooms do not have high-speed Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 160 rentals in the Super Saver class, 50 rentals in the Deluxe class, and 40 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. 1. **Use linear programming to determine how many reservations to accept in each rental class and how the…

Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Room Туре І Type II Super Saver $30 Rental Class $20 Deluxe $35 I $30 Business Type I rooms do not have high-speed Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 140 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. $40 (a) Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Is the demand by…

In the past, Peter Kelle's tire dealership in Baton Rouge sold an average of 1,000 radials each year. In the past 2 years, 200 and 260, respectively were sold in fall, 340 and 300 in winter, 150 and 175 in spring, and 300 and 275 in summer. With a major expansion planned, kelle projects sales next year to increase to 1,200 radials. Based on next year's projected sales, the demand for each season is going to be (enter your responses as whole numbers): Season Fall Demand