A company is refurbishing smartphones out of used smartphones. They are able to produce three different quality levels (Gold, Silver, and Bronze). The revenue for selling x, y, and z units of the respective devices can be calculated as R(x, y, z) = 600x + 400y + 300z – x2 – y? – 22. In order to refurbish the devices, they need to run through fine-tuned automated machines and have to pass a final quality check, which is done by employees. The required time for these two processes per quality level and the daily available machine and employee working times are displayed in the following table: machine minutes employee minutes Gold 60 Silver 40 Bronze 30 daily available time 800 100 The company wants to maximize the daily profit while using all available resources. Please calculate the critical points of that optimization problem. What is the respective revenue?
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- Suppose that GLC earns a 2000 profit each time a person buys a car. We want to determine how the expected profit earned from a customer depends on the quality of GLCs cars. We assume a typical customer will purchase 10 cars during her lifetime. She will purchase a car now (year 1) and then purchase a car every five yearsduring year 6, year 11, and so on. For simplicity, we assume that Hundo is GLCs only competitor. We also assume that if the consumer is satisfied with the car she purchases, she will buy her next car from the same company, but if she is not satisfied, she will buy her next car from the other company. Hundo produces cars that satisfy 80% of its customers. Currently, GLC produces cars that also satisfy 80% of its customers. Consider a customer whose first car is a GLC car. If profits are discounted at 10% annually, use simulation to estimate the value of this customer to GLC. Also estimate the value of a customer to GLC if it can raise its customer satisfaction rating to 85%, to 90%, or to 95%. You can interpret the satisfaction value as the probability that a customer will not switch companies.Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)Use the RAND function and the Copy command to generate 100 random numbers. a. What fraction of the random numbers are smaller than 0.5? b. What fraction of the time is a random number less than 0.5 followed by a random number greater than 0.5? c. What fraction of the random numbers are larger than 0.8? d. Freeze these random numbers. However, instead of pasting them over the original random numbers, paste them onto a new range. Then press the F9 recalculate key. The original random numbers should change, but the pasted copy should remain the same.
- A suburb of Dayton, Ohio, has four local dry cleaners that compete with each other on the basis of price and service speed. Each of them can perform the same basic services at the same level of quality. The following table provides the price that each dry cleaner charges to clean a two-piece suit, as well as the quoted number of days that the service will take. Dry Cleaner Price Number of Days A $ 8.00 3 B $ 9.50 3 C $ 9.00 2 D $ 7.50 4 Which of these dry cleaners are NOT on the efficient frontier?Deborah Kellogg buys Breathalyzer test sets for the Winter Park Police Department. The quality of the test sets from her two suppliers is indicated in the following table: For example, the probability of getting a batch of tests that are 1% defective from Winter Park Technology is .70. Because Kellogg orders 10,000 tests per order, this would mean that there is a .70 probability of getting 100 defective tests out of the 10,000 tests if Winter Park Technology is used to fill the order. A defective Breathalyzer test set can be repaired for $0.50. Although the quality of the test sets of the second supplier, Dayton Enterprises, is lower, it will sell an order of 10,000 test sets for $37 less than Winter Park. a) Develop a decision tree. b) Which supplier should Kellogg use?Deborah Kellogg buys Breathalyzer test sets for the Winter Park Police Department. The quality of the test sets from her two suppliers is indicated in the following table: For example, the probability of getting a batch of tests that are 1% defective from Winter Park Technology is .70. Because Kellogg orders 10,000 tests per order, this would mean that there is a .70 probability of getting 100 defective tests out of the 10,000 tests if Winter Park Technology is used to fill the order. A defective Breathalyzer test set can be repaired for $0.50. Although the quality of the test sets of the second supplier, Dayton Enterprises, is lower, it will sell an order of 10,000 test sets for $37 less than Winter Park. a) Develop a Decision Treeb) Which supplier should Kellog use? Percent Defective Probability for Winter Park Technology Probability for Dayton Enterprises 1 0.70 0.30 3 0.20 0.30 5 0.10 0.40
- A manufacturer of programmable calculators is attempting to determine a reasonable free-service period for a model it will introduce shortly. The manager of product testing has indicated that the calculators have an expected life of 30 months. Assume product life can be described by an exponential distribution. T / MTBF e-T /MTBF T / MTBF e-T /MTBF T / MTBF e-T /MTBF 0.10 0.9048 2.60 0.0743 5.10 0.0061 0.20 0.8187 2.70 0.0672 5.20 0.0055 0.30 0.7408 2.80 0.0608 5.30 0.0050 0.40 0.6703 2.90 0.0550 5.40 0.0045 0.50 0.6065 3.00 0.0498 5.50 0.0041 0.60 0.5488 3.10 0.0450 5.60 0.0037 0.70 0.4966 3.20 0.0408 5.70 0.0033 0.80 0.4493 3.30 0.0369 5.80 0.0030 0.90 0.4066 3.40 0.0334 5.90 0.0027 1.00 0.3679 3.50 0.0302 6.00 0.0025 1.10 0.3329 3.60 0.0273 6.10 0.0022 1.20 0.3012 3.70 0.0247 6.20 0.0020 1.30 0.2725 3.80 0.0224 6.30 0.0018 1.40 0.2466 3.90 0.0202 6.40 0.0017 1.50 0.2231 4.00 0.0183 6.50 0.0015 1.60 0.2019 4.10 0.0166 6.60 0.0014 1.70 0.1827 4.20…For a particular process, originally each 200 units of product manufactured yielded 180 conforming units, 9 units that must be scrapped, and the remaining units that must be reprocessed. Each scrapped unit results in a $30 loss and each reprocessed unit requires an extra 0.45 hours of processing time. The resource time of producing the original 200 units is 30 hours. As a result of a quality improvement program that was recently introduced, for each 200 units manufactured, the process now yields 190 conforming units, 4 unit to be scrapped, and the remaining units that must be reprocessed. Calculate the productivity (in units per hour) for the original process.Hi is this correct?The management of an oil company is trying to decide whether to drill for oil in a particular fieldin the Gulf of Mexico. It costs the company $600 thousand to drill in the selected field. Themanagement believes that if oil is found in this field, its estimated value will be $3400 thousand. Atpresent, this oil company believes that there is a 45% chance that the selected field actually containsoil. Before drilling, the oil company can hire a team of geologists to perform seismographic tests at acost of $55 thousand. Based on similar tests in other fields, the tests have a 25% false negative rate(no oil predicted when oil is present) and a 15% false positive rate (oil predicted when no oil ispresent).A. Assume the oil company wants to maximize its expected net earnings. Please utilize decisiontree analysis to determine its optimal strategy.B. Calculate the expected value of the information (EVI/EVSI) provided by the team ofgeologists.C. Calculate and interpret EVPI…
- A calculus instructor uses computer-aided instruction and allows students to take the midterm exam as many times as needed until a passing grade is obtained. Following is a record of the number of students in a class of 50 who took the test each number of times. Students Number of Tests 22 1 15 2 8 3 5 4 a.Find the expected value of the number of tests taken. b.Compute the variance and the standard deviation of the number of tests taken.A hardware company sells a lot of low-cost, high volume products. For one such product, it is equally likely that annual unit sales will be low or high. If sales are low (30,000), the company can sell the product for $20 per unit. If sales are high (70,000), a competitor will enter and the company will be able to sell the product for only $15 per unit. The variable cost per unit has a 20% chance of being $10, a 60% chance of being $11, and a 20% chance of being $12. Annual fixed costs are $20,000.a. Use simulation to estimate the company’s expected annual profit.b. Find a 95% interval for the company’s annual profit, that is, an interval such that about 95% of the actual profits are inside it.c. Now suppose that annual unit sales, variable cost, and unit price are equal to their respective expected values—that is, there is no uncertainty. Determine the company’s annual profit for this scenario. d. Can you conclude from the results in parts a and c that the expected profit from a…Which of the following statements is correct regarding the EMH form? Select one: None of the answers are correct If the market is weak-form efficient, then it is also semistrong and strong-form efficient. If the market is semistrong form efficient, then it is also strong form efficient If a market is strong-form efficient, it is also semistrong and weak form efficient If the market is strong-form efficient, it is also semistrong but not weak-form efficient