Asilekpe Company Limited is considering constructing a borehole in the village of Adukofe. The construction would cost Gh₵2 million and there will be no cost of maintenance. The following table shows the company’s anticipated demand over the lifetime of the bridge:Price per gallon (Gh₵)Number of gallons8071000006200000530000044000003500000260000017000000800000a. If the company were to construct the borehole what would be its profit-maximizing price? Would that be the efficient level of output? Explain your answer.b. If the company is interested in maximizing profit, should it construct the borehole? What would be its profit or loss?c. If the government were to construct the borehole, what price should it charge?d. Should the government construct the borehole? Explain.

The price at which highest amount of profit is possible is known as profit-maximizing price. An…

Answered: be no cost of maintenance. The…

Business

Operations Management

be no cost of maintenance. The following table shows the company’s anticipated demand over the lifetime of the bridge

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 45P

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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?
It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
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?
Six months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of 150 per room. The AMA believes the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of 250 per room. a. Use simulation with @RISK to determine the number of rooms that should be reserved to minimize the expected cost to the AMA. Try possible values from 4100 to 4900 in increments of 100. b. Redo part a for the case where the number attending has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. Does this change the substantive results from part a?
PROBLEM The management of the Book Warehouse Company wishes to apply the Miller-Orr model to manage its cash investment. They have determined that the cost of either investing in or selling marketable securities is $100. By looking at Book Warehouse’s past cash needs, they have determined that the variance of daily cash flows is $20,000. Book Warehouse’s opportunity cost of cash, per day, is estimated to be 0.03%. Based on experience, management has determined that the cash balance should never fall below $10,000. 1. How much is the cost per transaction?(Use a number, no decimal value, no commas, no currency, no space) * 2. How much is the return point based on the Miller-Orr model of cash management? (Use a number, no decimal value, no commas, no currency, no space) * 3. How much is the upper limit based on the Miller-Orr model of cash management?(Use a number, no decimal value, no commas, no currency, no space) * PLEASE ANSWER ALL QUESTIONS. THANKS!
Global Logistics needs to rent space for storing product for the next three years. The following information regarding the demand and spot price is available. Current demand for the product is 150,000. Historically, Global Logistics has required 1500 square feet to store 1500 units of the product. Demand for the product can go up by 20% with a probability of 0.7 or down by 20% with a probability of 0.3. Global Logistics can sign a three-year fixed lease to rent 150,000 square feet of space at $1.00 per square foot per year. The firm may also choose to obtain warehousing space on the spot market. The current spot market price is $1.20 per square foot per year. The spot price can go up by 10% with a probability of 0.8 and can decrease by 10% with a probability of 0.2. The firm receives a revenue of $1.22 for each unit of demand. a) Create a decision tree showing period 0, 1 and 2 for the scenario described above. b) Calculate the NPV for the option when the firm decides to sign a…
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.
I need a detailed explanation and assistance to solve this problem: Wineco produces wine cooler as a blend of wine, grape juice and apple juice ingredients, which it sells for $4 per gallon. The costs of ingredients are given in the following table: Cooler Ingredient Price per Gallon ($) wines 1.20 grape juice 1.40 Apple juice 0.60 Wineco owns a blending plant with a production capacity of 200 gallons per day. Because the plant is fully automated, all other production costs are negligible by comparison to the cost of ingredients, and can be ignored. Government regulations mandate that wine cooler products must satisfy the following guidelines: At least 10% of the blend produced must be grape juice. The ratio of apple juice to grape juice in the blend produced must be 2.5:1 The blend produced must contain between 20% and 25% wine. Wineco wishes to use LP in order to determine the quantities of ingredients to buy for a day’s production of wine cooler, so…
Travel Co. specializes in trans-American moves for businesses and individuals through the shipment of containers. For every container the company transports via rail, Travel Co. must pay the rail owners $5,000. In addition, containers are weighed and for each pound of weight, the company must pay $0.40. Harry plans to charge $0.68 per pound to his customers. How many pounds would a container have to hold in order for the company to Break Even? What would the total revenue be at Break Even? The company finds out that to maintain the integrity of its containers, each container could only hold an average of 16,000 pounds. What would the company have to charge customers to make $7,000 in profit on each container?
PROBLEM The Seminole Company wishes to apply the Miller-Orr model to manage its cash investment. Seminole’s management has determined that the cost of either investing in or selling marketable securities is $200. By looking at Seminole Company’s past cash needs, they have determined that the variance of daily cash flows is $10,000. Seminole Company’s opportunity cost of cash, per day, is estimated to be 0.05%. Seminole management has figured, based on their experience dealing with the cash flows of the company, that there should be a cushion— a safety stock—of cash of $20,000. 1. How much is the variance of daily cash flows? (Use a number, no decimal value, no commas, no currency, no space) * 2. How much is the opportunity cost of cash, per day? (Use a number, must be in decimal form. eg. 6.3%/100, encode 0.063 , no commas, no currency, no space) * 3. How much is the cost per transaction? (Use a number, no decimal value, no commas, no currency, no space) * PLEASE ANSWER ALL QUESTIONS.…
Larry’s Bakery operates a chain of ten high-end bakeries. Larry, the owner of these amazing bakeries, is looking at two options to increase his revenues throughout his chain of bakeries. The first option is to launch a loyalty card. Doing this would cost Larry $500,000. The probability that this would result in high sales is 0.6, which means the probability it would result in low sales is 0.4. If high sales are generated from this option, Larry can expect to see additional revenues of $1,000,000. If low sales are generated from this option, Larry can expect to see additional revenues of only $750,000. The second option Larry has is to cut the prices throughout his bakeries. Doing so would cost him $300,000. The probability that this would result in high sales is 0.8. If doing this results in high sales, Larry can expect to see additional revenues of $800,000. If it results in low sales, he can expect to see additional revenues of only $500,000. Larry obviously has a tough decision…