Draw a decision tree for Mr. Sakala indicating all choices and events What decision Mr. Sakala should take regarding the investment of K100,000? If Mr. Sakala is a risk averter, should he change the decision given by you?
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OPERATIONS RESEARCH TWO
Sakala is interested in developing and marketing a new drug. The cost of extensive research to develop the drug would be K100,000. The manager of research programme said that there is 60% chance that the drug will be developed successfully. The market potential is assessed as follows with present value of profit:
|
Market conditions |
Probability |
Present value of profits (K) |
|
Large market potential |
0.1 |
500,000 |
|
Moderate market potential |
0.6 |
220,000 |
|
Low market potential |
0.3 |
80,000 |
The present value figures do not include the cost of research. While Mr. Sakala was considering this proposal, another similar proposal came up which also required the investment of K100,000 .The present value of profit for the second proposal wasK120,000. The
- Draw a decision tree for Mr. Sakala indicating all choices and events
- What decision Mr. Sakala should take regarding the investment of K100,000?
- If Mr. Sakala is a risk averter, should he change the decision given by you?
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- 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.The CEO of Lucky Petroleum Co. has been considering to open a new gasoline statioin. He must decide how large the station should be. The annual returns (IDR billions) will depend on both the size of the station and market factor. After a careful analysis he developed the following table: Size of Station Good Market Fair Market Poor Market Small 50 20 -10 Medium 70 30 -20 Large 100 50 -30 Probability 0.5 0.3 0.2 Compute the expected value of each alternative size of station, and select the best decision. Construct the opportunity loss table and determine the best decision. Compute the expected value of perfect information.
- Kroft Food Products is attempting to decide whether it should introduce a new line of salad dressings called Special Choices. The company can test market the salad dressings in selected geographic areas or bypass the test market and introduce the product nationally. The cost of the test market is $150,000. If the company conducts the test market, it must wait to see the results before deciding whether to introduce the salad dressings nationally. The probability of a positive test market result is estimated to be 0.6. Alternatively, the company can decide not to conduct the test market and go ahead and make the decision to introduce the dressings or not. If the salad dressings are introduced nationally and are a success, the company estimates that it will realize an annual profit of $1.6 million, whereas if the dressings fail, it will incur a loss of $700,000. The company believes the probability of success for the salad dressings is 0.50 if they are introduced without the test market.…Gotham City has 10,000 streetlights. City investigatorshave determined that at any given time, an average of 1,000lights are burned out. A streetlight burns out after an averageof 100 days of use. The city has hired Mafia, Inc., to replaceburned-out lamps. Mafia, Inc.’s contract states that thecompany is supposed to replace a burned-out street lamp inan average of 7 days. Do you think that Mafia, Inc. is livingup to the contract?The Wisteria University athletic department is considering a campaign next year to raise funds for a new athletic field. To a large extent, the response to the campaign depends on how successful the soccer team is in the fall. In the past they have had winning seasons 60% of the time. If they have a winning season (G), many alumni will contribute and the campaign will raise $3 million. If they have a losing season (P), very few will contribute and they will lose $2 million. If the campaign does not take place, no cost is incurred. On September 1, prior to the start of the season, the athletics department must decide whether to conduct the campaign next year. a) Develop a decision tree formulation for this problem by identifying the alternative options, the states of nature, and the payoff matrix. b) According to the maximum expected value rule, should the campaign be conducted? c) What is the VEIP? d) A famous soccer guru, William Walsh, has offered to evaluate whether the team…
- The Wisteria University athletic department is considering a campaign next year to raise funds for a new athletic field. To a large extent, the response to the campaign depends on how successful the soccer team is in the fall. In the past they have had winning seasons 60% of the time. If they have a winning season (G), many alumni will contribute and the campaign will raise $3 million. If they have a losing season (P), very few will contribute and they will lose $2 million. If the campaign does not take place, no cost is incurred. On September 1, prior to the start of the season, the athletics department must decide whether to conduct the campaign next year. d) A famous soccer guru, William Walsh, has offered to evaluate whether the team will have a winning season. For $100,000 he will evaluate the team's spring and preseason practices. William will give his prediction on September 1 as to what type of season, G or P, the team will have. In similar situations in the past, when…The Wisteria University athletic department is considering a campaign next year to raise funds for a new athletic field. To a large extent, the response to the campaign depends on how successful the soccer team is in the fall. In the past they have had winning seasons 60% of the time. If they have a winning season (G), many alumni will contribute and the campaign will raise $3 million. If they have a losing season (P), very few will contribute and they will lose $2 million. If the campaign does not take place, no cost is incurred. On September 1, prior to the start of the season, the athletics department must decide whether to conduct the campaign next year. d) A famous soccer guru, William Walsh, has offered to evaluate whether the team will have a winning season. For $100,000 he will evaluate the team's spring and preseason practices. William will give his prediction on September 1 as to what type of season, G or P, the team will have. In similar situations in the past, when…See the answer A local movie studio wants to determine which of two new scripts they should select for their next major production. The manager feels that script #1 has a 70% chance of earning Php100 million over the long run, but a 30% chance of losing Php20 million. If this movie is successful, then a sequel could also be produced, with an 80% chance of earning Php50 million, but a 20% chance of losing Php10 million. On the other hand, she feels that script #2 has a 60 % chance of earning Php120 million, but a 40% chance of losing Php30 million. If successful, its sequel would have a 50% chance of earning $80 million and a 50% chance of losing Php40 million. As with the first script, if the original movie is a "flop," then no sequel would be produced. What is the expected payoff from selecting script #2?
- Define the decision variables ,Formulate the objective function, Formulate the constraints Sears Investment has $250,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 8% return or in municipal bonds at an average rate of return of 9%. Bank regulations require diversification to the extent that a t least 50% of the investment be placed in Treasury notes. Because of defaults in such municipalities as California and Texas, it is decided that no more than 40% of the investment be placed in bonds. How much should Sears Investment invest in each security so as to maximize its return on investment?Carlisle Tire and Rubber, Inc., is considering expanding production to meet potential increases in the demand for one of its tire products. Carlisle’s alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. The market for this particular tire product may expand, remain stable, or contract. Carlisle’s marketing department estimates the probabilities of these market outcomes to be 0.25, 0.35, and 0.40, respectively. The file P06_31.xlsx (picture of given excel file is attached) contains Carlisle’s payoffs and costs for the various combinations of decisions and outcomes. Identify the strategy that maximizes this tire manufacturer’s expected profit. Perform a sensitivity analysis on the optimal decision, letting each of the monetary inputs vary one at a time plus or minus 10% from its base value, and summarize your findings. Which of the inputs appears to have the largest effect on the best solution?Garfield Industries is expanding its operations throughout the Southeast United States. Garfield anticipates that the expansion will increase sales by $1,000,000 and increase operating costs (excluding depreciation and amortization) by $700,000. Depreciation and amortization expenses will rise by $50,000, interest expense will increase by $150,000, and the company’s tax rate will remain at 40 percent. If the company’s forecast is correct, how much will net income increase or decrease, as a result of the expansion?