The yearly demand for a seasonal, profitable item follows the distribution:Demand (units) Probability1,000202,000303,000404,00010A manufacturer is considering launching a project to produce this item and could produce it by oneof three methods:A. (10%). Use existing tools at a cost of S6 per unit.B. (10%). Buy cheap, special equipment for $1,000. The value of the equipment at the end of theyear (salvage value) is zero. The cost would be reduced to $3 per unit.C. (10%). Buy high-quality, special equipment for $10,000 that can be depreciated over four years(one fourth of the cost each year). The cost with this equipment would be only S2 per unit.Set up this project as a decision tree to find whether the manufacturer should approve this project,and if so, which method of production to use to maximize profit. Hint: Compare total annual costs.Assume that production must meet all demand; each unit demanded and sold means more profit.

Answered: Set up this project as a decision tree…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 63P: It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield...

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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.
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.
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.
Downtown Health Clinic needs to order influenza vaccines for the next flu season. The Clinic charges its patients $15.00 per vaccination and each dose of vaccine costs the clinic $4.00 to purchase. The Center for Disease Control has a long standing policy of buying back unused vaccines for $1.00 per dose. The Clinic estimates the following probability distribution for the season’s demand:Demand Probability2,000 0.053,000 0.204,000 0.255,000 0.406,000 0.10a. How many vaccines should the Clinic order to maximize its expected profit?b. The Clinic is trying to determine if they should participate in a new Federal program in which the cost of each dose is reduced to $2.00. However, to participate in the program, they can charge no more than $10.00 per vaccine. On strictly a profit maximizing basis, should the Clinic agree to participate?
A company sells its products to wholesalers in batches of 1,000 units only. The daily demand for its product and the respective probabilities are given below. Demand (Units) Probability 0 0.1 1000 0.3 2000 0.4 3000 0.1 4000 0.1 a. Determine the expected daily demand. b. Assume that the company sells its product at $3.90 per unit. What is the expected daily revenue?
Suppose we are considering the question of how much capacity to build in the face of uncertain demand. Assume that the cost is $20 per unit of lost sales due to insufficient capacity. Also assume that there is a cost of $7 for each unit of capacity built. The probability of various demand levels is as follows: Demand—X Units Probability of X 0 .05 1 .10 2 .15 3 .20 4 .20 5 .15 6 .10 7 .05 a. How many units of capacity should be built to minimize the total cost of providing capacity plus lost sales? b. State a…
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Daniel Grady is thefinancial advisor for a number of professional athletes.An analysis of the long-term goals for many of theseathletes has resulted in a recommendation to purchasestocks with some of the income that they have set aside for investments. Five stocks have been identified as hav-ing very favorable expectations for future performance. Although the expected return is important in theseinvestments, the risk, as measured by the beta of the stock, is also important. (A high value of beta indicatesthat the stock has a relatively high risk.) The expectedreturn and the beta for five stocks are as follows: Stock 1 2 3 4 5 Expected Return (%) 11.0 9.0 6.5 15.0 13.0 Beta 1.20 0.85 0.55 1.40 1.25 Daniel would like to minimize the beta of the stockportfolio (calculated using a weighted average ofthe amounts put into the different stocks) whilemaintaining an expected return of at least 11%.Since future conditions may change, Daniel hasdecided that no more than 35% of the…
6. Laura is trying to decide whether to sell her knitted hats on Etsy, at a holiday bazaar, or in a local boutique. Demand could be 0 hats/month, 10 hats/month, or 20 hats/month. Given the payoff matrix below, what is her decision under equally likely? Demand = 0 Demand = 10 Demand = 20 Etsy -$70 $80 $230 Bazaar -$60 $90 $240 Boutique -$80 $70 $220 Select one: a. Etsy and boutique. b. Etsy only. c. Etsy and bazaar. d. Bazaar and boutique. e. All 3 are equally good. f. Bazaar only. g. None of them are good options. h. Boutique only.
Option 2: Raise prices by 50%. If this occurs, there is a 75% chance that an Entrepreneur will set up in competition this year. The board’s estimate of its annual profit in this situation would be as follows: 2A: With new competitor 2B: Without new competitor Probability Profit (Sh.) Probability Profit (Sh.) 0.25 150,000 0.5 200,000 0.5 120,000 0.3 150,000 0.25 80,000 0.2 100,000 Option 3: Expand the car park quickly at a cost of Sh. 50,000 keeping prices theSame. The profits are then estimated to be like 2B above, except that the probabilities would be 0.6, 0.3 and 0.1 respectively. Required: Draw a decision tree for the above problem, including all the relevant data. Using expected values analyze the decision tree and recommend the best option to the owners of the car park.
Harley, an ice-cream vendor, purchases each pint of ice-cream for $7 and sells for $20 each. At the end of the week, the unsold ice-cream can be salvaged for $2 each. From past experience, Harley has estimated the sales probabilities as below. What is the optimal number of pints Harley should purchase? Number of Ice-creams Sold, Probability 1 = 0.05, 2 = 0.1, 3 = 0.2 , 4 = 0.25, 5 = 0.15, 6 = 0.1, 7 = 0.08, 8 = 0.07
The Math Club is selling pies on March 14th as a fundraiser. Let Q be the number of pies they make and sell. The total cost, C(Q) in dollars, for making Q pies is given by: C(Q) = 36 + 2Q. Sales price is 5 dollars for each pie. What is the additional cost to make 21 pies instead of 20 pies?

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Set up this project as a decision tree to find whether the manufacturer should approve this project, and if so, which method of production to use to maximize profit. Hint: Compare total annual costs. Assume that production must meet all demand; each unit demanded and sold means more profit.