A veterinarian has been asked to prepare a diet for a group of dogs to be used in a nutrition study at the School of Animal Science. It has been stipulated that each serving should be no larger than 9 oz and must contain at least 29 units of Nutrient I and 20 units of Nutrient II. The vet has decided that the diet may be prepared from two brands of dog food: Brand A and Brand B. Each ounce of Brand A contains 3 units of Nutrient I and 4 units of Nutrient II. Each ounce of Brand B contains 5 units of Nutrient I and 2 units of Nutrient II. Brand A costs 3 cents/oz and Brand B costs 4 cents/oz. Determine how many ounces of each brand of dog food should be used per serving to meet the given requirements at a minimum cost. Brand A Brand B Xoz xoz What is the minimum cost per serving? x cents

A veterinarian has been asked to prepare a diet for a group of dogs to be used in a nutrition study at the School of Animal Science. It has been stipulated that each serving should be no larger than 9 oz and must contain at least 29 units of Nutrient I and 20 units of Nutrient II. The vet has decided that the diet may be prepared from two brands of dog food: Brand A and Brand B. Each ounce of Brand A contains 3 units of Nutrient I and 4 units of Nutrient II. Each ounce of Brand B contains 5 units of Nutrient I and 2 units of Nutrient II. Brand A costs 3 cents/oz and Brand B costs 4 cents/oz. Determine how many ounces of each brand of dog food should be used per serving to meet the given requirements at a minimum cost. Brand A Brand B Xoz xoz What is the minimum cost per serving? x cents

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 69P: The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon...

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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.
Digital Controis, Inc. (DCI), manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus 1 mile per hour, whereas the smaller model B has an accuracy of plus or minus 3 miles per hour. For the next week, the company has orders for 100 units of model A and 150 units of model B. Although DCI purchases all the electronic components used in both models, the plastic cases for both models are manufactured at a DCI plant in Newark, New Jersey. Each model A case requires 4 minutes of injection-molding time and 6 minutes of assembly time. Each model B case requires 3 minutes of injection-molding time and 8 minutes of assembly time. For next week, the Newark plant has 600 minutes of injection-molding time avallable and 1,080 minutes of assembly time availab The manufacturing cost is $10 per case for model A and $6 per case for model B. Depending upon demand and the time avalable at the Newark plant, DCI occasionally…
Ralf Bohle GmbH, a German manufacturing company, produces bicycle and wheelchair tires under the Schwalbe Tire brand name. Road and racing cyclists require specific tires that meet demanding specifications, and Ralf Bohle is concerned about monitoring the width of its road tires for these picky consumers. The company has a lower specification limit of 23 mm and an upper specification limit of 24 mm for the width of their flagship Schwlbe Pro One TT racing tire. After monitoring their process for some time, the company determines that the widths of tires produced is normally distributed with a standard deviation in width of 0.33 mm and a mean of 23.5 mm wide. a) What is the process capability index for the process? ) Assume the standard formulation for process capability where ?? = 1 refers to a threesigma process (i.e. ?? = 1 means that the upper and lower specification limits span ± 3?). b) What is the probability that a tire will either be too wide or too narrow? Stated differently,…
Some citizens complained to city council members that there should be equal protection under the law against the occurrence of crimes. The citizens argued that this equal protection should be interpreted as indicating that high-crime areas should have more police protection than low-crime areas. Therefore, police patrols and other methods for preventing crime (such as street lighting or cleaning up abandoned areas and buildings) should be used proportionately to crime occurrence. The city has been broken down into 20 geographic areas, each containing 5,000 residences. The police recognize that not all crimes and offenses are reported: people do not want to become involved, consider the offenses too small to report, are too embarrassed to make a police report, or do not take the time, among other reasons. Every month, because of this, the police are contacting by phone a random sample of 800 of the 5,000 residences for data on crime. (Respondents are guaranteed anonymity.) The 800…
Some citizens complained to city council members that there should be equal protection under the law against the occurrence of crimes. The citizens argued that this equal protection should be interpreted as indicating that high-crime areas should have more police protection than low-crime areas. Therefore, police patrols and other methods for preventing crime (such as street lighting or cleaning up abandoned areas and buildings) should be used proportionately to crime occurrence. The city has been broken down into 20 geographic areas, each containing 5,000 residences. The police recognize that not all crimes and offenses are reported: people do not want to become involved, consider the offenses too small to report, are too embarrassed to make a police report, or do not take the time, among other reasons. Every month, because of this, the police are contacting by phone a random sample of 1,000 of the 5,000 residences for data on crime. (Respondents are guaranteed anonymity.) The 1,000…
As part of a quality improvement initiative, Enterprise Technology employeescomplete a three-day training program on teaming and a two-day training programon problem-solving. The manager of quality improvement has requested that atleast eight training programs on teaming and at least ten training programs on problem-solving be offered during the next six months. In addition, senior-level managementhas specified that at least twenty-five training programs must be offered during this period.Enterprise Technology hires a consultant to teach the training programs. Duringthe next quarter, the consultant has eighty-four days of training time available. Each trainingprogram on teaming costs ten-thousand dollars and each training program on problem-solvingcosts eight thousand dollars. a. First step is to formulate a linear programming model that can be used to determine thenumber of training programs on teaming and the number of training programs onproblem-solving that should be offered in…
Employees at Precision Engine Parts Company produce parts according to exact design specifications. The employees are paid according to a piece-rate system, wherein the faster they work and the more parts they produce, the greater their chances for monthly bonuses. Management suspects that this method of pay may contribute to an increased number of defective parts. A specific part requires a normal, standard time of 23 minutes to produce. The quality control manager has checked the actual average times to produce this part for 10 different employees during 20 days selected at random during the past month and determined the corresponding percentage of defective parts, as follows: Develop a linear regression model relating average production time to percentage defects to determine whether a relationship exists and the percentage of defective items that would be expected with a normal production time of 23 minutes.
As part of a quality improvement initiative, Consolidated Electronics employees complete a three-day training program on teaming and a two-day training program on problem-solving. The manager of quality improvement has requested that at least 8 training programs on teaming and at least 10 training programs on problem-solving should be offered during the next six months. In addition, senior-level management has specified that at least 25 training programs must be offered during this period. Consolidated Electronics uses a consultant to teach the training programs. During the next quarter, the consultant has 84 days of training time available. Each training program on teaming costs P10,000 and each training program on problem-solving costs P8,000. Formulate a linear programming model that can be used to determine the number of training programs on teaming and the number of training programs on problem-solving that should be offered in order to minimize total cost. Graph the feasible…
As part of a quality improvement initiative, Consolidated Electronics employees complete a three-day training program on teaming and a two-day training program on problem-solving. The manager of quality improvement has requested that at least 8 training programs on teaming and at least 10 training programs on problem-solving be offered during the next six months. In addition, senior-level management has specified that at least 25 training programs must be offered during this period. Consolidated Electronics uses a consultant to teach the training programs. During the next quarter, the consultant has 84 days of training time available. Each training program on teaming costs $10,000 and each training program on problem-solving costs $8,000. a. Formulate a linear programming model that can be used to determine the number of training programs on teaming and the number of training programs on problem-solving that should be offered in order to minimize total cost.b. Graph the feasible…
The Collector's Choice Inc. (CCI), a luxury car import company, has an old warehouse at the Port of Miami, Florida, where it temporarily stores expensive sports cars and automotive parts that arrive from Europe. This summer, CCI has noticed that the termite infestation in the warehouse has escalated to a point where tenting cannot be postponed anymore. (Tenting is the process of wrapping a building inside a huge tent that is subsequently filled with a poisonous gas capable of killing most forms of life inside, including insects, plants, pets, and human beings.) CCI's pest control company's contract specifies a to-do list of pre-tenting tasks, which include: • Turning off all air-conditioning units and opening all windows of the warehouse • Turning off all internal and external lights, including those operating on a timer • Pruning all outdoor vegetation at least 18" away from the -warehouse • Soaking the soil around the warehouse on the first day of tenting The requirement of opening…
The State of Virginia has instituted a series of Standards ofLearning (SOL) tests in math, history, English, and sciencethat all high school students must pass with a grade of 70 be-fore that are allowed to graduate and receive their diploma.The school superintendent of Montgomery County believesthe tests are unfair because they are closely related to teachersalaries and teacher school tenure (i.e., the years a teacher hasbeen at a school). The superintendent has sampled 12 othercounty school systems in the state and accumulated thefollowing data for average teacher salaries and averageteacher tenure.a. Using Excel, develop the multiple regression equationfor these data.b. What is the coefficient of determination for thisregression equation? Do you think the superintendentis correct in his beliefs?c. Montgomery County has an average SOL score of 74with an average teacher’s salary of $27,500 and anaverage teacher tenure of 7.8 years. The superintendenthas proposed to the school board a…
The Real Estate Settlement Procedures Act applies to: Group of answer choices commercial loans. junior liens. first mortgages and trust deeds. loans for vacant land.