Hannah Byers and Kathleen Taylor are considering the possibility of teaching swimming to kids during the summer. A local swim club opens its pool at noon each day, so it is available to rent during the morning. The cost of renting the pool during the 10-week period for which Hannah and Kathleen would need it is $1,700. The pool would also charge Hannah and Kathleen an admis- sion, towel service, and life guarding fee of $7 per pupil, and Hannah and Kathleen estimate an additional $5 cost per student to hire several assistants. Hannah and Kathleen plan to charge $75 per student for the 10-week swimming class. a. How many pupils do Hannah and Kathleen need to enroll in their class to break even? b. If Hannah and Kathleen want to make a profit of $5,000 for the summer, how many pupils do they need to enroll? c. Hannah and Kathleen estimate that they might not be able to enroll more than 60 pupils. If they enroll this many pupils, how much would they need to charge per pupil to realize their profit goal of $5,000?
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- 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?Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.Larissa Warren, the owner of East Coast Yachts, has been in discussions with a yacht dealer in Monaco about selling the company’s yachts in Europe. Jarek Jachowicz, the dealer, wants to add East Coast Yachts to his current retail line. Jarek has told Larissa that he feels the retail sales will be approximately €8 million per month. All sales will be made in euros, and Jarek will retain 5 percent of the retail sales as commission, which will be paid in euros. Because the yachts will be customized to order, the first sales will take place in one month. Jarek will pay East Coast Yachts for the order 90 days after it is filled. This payment schedule will continue for the length of the contract between the two companies. Larissa is confident the company can handle the extra volume with its existing facilities, but she is unsure about any potential financial risks of selling yachts in Europe. In her discussion with Jarek, she found that the current exchange rate is $1.34/€. At this exchange…
- Julia Robertson is a senior at Tech, and she’s investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game, and Julia knows, from attending the games herself, that everyone eats a lot of food. She has to pay $1,000 per game for a booth, and the booths are not very large. Vendors can sell either food or drinks on Tech property, but not both. Only the Tech athletic department concession stands can sell both inside the stadium. She thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans, and so these are the items she would sell. Most food items are sold during the hour before the game starts and during halftime; thus it will not be possible for Julia to prepare the food while she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $600 she can lease a warming oven for…During the summer, Olympic swimmer Adam Johnsonswims every day. On sunny summer days, he goes to anoutdoor pool, where he may swim for no charge. On rainydays, he must go to a domed pool. At the beginning of thesummer, he has the option of purchasing a $15 season passto the domed pool, which allows him use for the entiresummer. If he doesn’t buy the season pass, he must pay $1each time he goes there. Past meteorological records indicatethat there is a 60% chance that the summer will be sunny(in which case there is an average of 6 rainy days during thesummer) and a 40% chance the summer will be rainy (anaverage of 30 rainy days during the summer).Before the summer begins, Adam has the option ofpurchasing a long-range weather forecast for $1. Theforecast predicts a sunny summer 80% of the time and arainy summer 20% of the time. If the forecast predicts asunny summer, there is a 70% chance that the summer willactually be sunny. If the forecast predicts a rainy summer,there is an 80%…Travis Kellogg is a sales representative for Xerox and his territory includes St. Louis and the surrounding suburbs. One of his accounts is Cintas, which offers a wide range of products to businesses. Travis was working with the Cintas division manager, Kiera Valentine, to gain her approval to purchase a networked printer and copier for the local office. The price of the printer/copier including installation would be $5,490, but Kiera has a spending limit of $5,000. She and Travis try to negotiate how Xerox can get the order and Kiera can get the printer but stay within her division’s budget. Eventually, they agreed to a deal of $5,000 for the printer/copier, plus Cintas would deliver and maintain welcome mats or rugs in Xerox’s St. Louis office. Travis and Kiera successfully utilized _____ to facilitate the exchange. A.trade B.credit C.money D.bartering E. negotiation
- Grocers Inc. is considering offering a purified water service through a contract company that would locate a machine on the inside of the market store. There are two contract companies Grocers Inc. is considering, ClearWater and PureVida. ClearWater would charge an annual lease fee of $800 for set-up of the machine and for this machine, there is a utility cost of $0.10 for every gallon of water dispensed and ClearWater charges $0.05 for maintenance. For PureVida, the annual lease fee is $700, the utility cost is $0.12 for every gallon and PureVida charges $0.06 for maintenance. Grocers Inc. customers would purchase refilled gallons of water for $0.97.a. What is the annual break-even point for each option?b. At what volume in number of gallons would the two options have the same cost?c. At what forecasted volume should Grocers Inc. select ClearWater and what volume should they select PureVida and why?Lauren Moore has sold her business for $500,000 and wants to invest in condominium units (which she intends to rent) and land (which she will lease to a farmer). She estimates that she will receive an annual return of $8,000 for each condominium and $6,000 for each acre of land. A condominium unit costs $70,000, and land costs $30,000 per acre. A condominium will cost her $1,000 per unit, an acre of land will cost $2,000 for maintenance and upkeep, and $14,000 has been budgeted for these annual expenses. Lauren wants to know how much to invest in condominiums and land to maximize her annual return. Requirements:a) Define decision variables and tabulated datab) Formulate the Integer Linear Programming Model.Lauren Moore has sold her business for $500,000 and wants to invest in condominium units (which she intends to rent) and land (which she will lease to a farmer). She estimates that she will receive an annual return of $8,000 for each condominium and $6,000 for each acre of land. A condominium unit costs $70,000, and land costs $30,000 per acre. A condominium will cost her $1,000 per unit, an acre of land will cost $2,000 for maintenance and upkeep, and $14,000 has been budgeted for these annual expenses. Lauren wants to know how much to invest in condominiums and land to maximize her annual return. a. Formulate a mixed integer programming model for this problem. b. Solve this model by using the computer.
- Lauren Moore has sold her business for $500,000 and wants to invest in condominium units (which she intends to rent) and land (which she will lease to a farmer). She estimates thatshe will receive an annual return of $8,000 for each condominium and $6,000 for each acre of land. A condominium unit costs $70,000, and land costs $30,000 per acre. A condominium will cost her $1,000 per unit. an acre of land will cost $2,000 for maintenance and upkeep, and $14,000 has been budgeted for these annual expenses. Lauren wants to know how much to invest in condominiums and land to maximize her annual return. a. Formulate a mixed integer programming model for this problem. b. Solve this model by using the computer.Noah Yobs, who has $75,400 of AGI (solely from wages) before considering rental activities, has $67,860 of losses from a real estate rental activity in which he actively participates. He also actively participates in another real estate rental activity from which he has $37,700 of income. He has other passive activity income of $24,128. a. What amount of rental loss can Noah use to offset active or portfolio income in the current year? 6,032 Compute Noah’s AGI on Form 1040 [pages 1 and 2; also complete Schedule 1 (Form 1040)] for the current year. Use the minus sign to indicate a loss.Erica is going to fly to London on August 5th and return home on August 20th. It is now July 1st. On July 1st, she may buy a one-way ticket (for $350) or a round-trip ticket (for $660). She may also wait until August 1st when a one-way ticket will cost $370 and a round-trip ticket $730. It is possible that between July 1st and August 1st, her sister (who works for the airline) will be able to obtain a free one-way ticket for Erica. The probability that her sister will obtain the free ticket is 0.3. If Erica has bought a round trip ticket on July 1st and her sister has obtained the free ticket, she may return “half” of her round-trip to the airline. In this case her total cost will be $330 plus a penalty of $50. Use a decision tree to determine Erica’s lowest expected cost of obtaining a round-trip ticket to London.