Along the Western coast of India, an oil tanker has fouled 100 miles of the shoreline. Fourteen days have been given to the oil company to clean up the shoreline after which a fine to the amount of Rs 100,000 will be levied per day. The local clean-up crew can scrub 5 miles of the beach per week at the cost of Rs 60,000 per day. Additional crews can be brought in at a cost of Rs 180,000 plus Rs 80,000 per day for each crew. (a) Determine the number of additional crews that the company should buy in order to minimise the total cost. Use the 5-step method described in class. What will be the total cost to the company? (b) Do a sensitivity analysis of the solution (optimal number of crews and the total cost) to the amount of fine levied and the rate at which a crew can clean up the shoreline.
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Along the Western coast of India, an oil tanker has fouled 100 miles of the shoreline. Fourteen days have been given to the oil company to clean up the shoreline after which a fine to the amount of Rs 100,000 will be levied per day. The local clean-up crew can scrub 5 miles of the beach per week at the cost of Rs 60,000 per day. Additional crews can be brought in at a cost of Rs 180,000 plus Rs 80,000 per day for each crew.
(a) Determine the number of additional crews that the company should buy in order to minimise the total cost. Use the 5-step method described in class. What will be the total cost to the company?
(b) Do a sensitivity analysis of the solution (optimal number of crews and the total cost) to the amount of fine levied and the rate at which a crew can clean up the shoreline.
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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.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?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…
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- The Reliance Manufacturing Company produces an aircraft part. The company can produce the part entirely at a flexible work center with multiple computerized machines. The company has four work centers, all of which are different because they were purchased at different times. Each work center has a single operator; however, the company’s operators have different skill levels, resulting in different levels of daily output and product quality. The following tables show the average daily output and average number of defects per day for each of the company’s five operators who are capable of producing the aircraft part: Average Daily Output per Machine Operator A B C D 1 18 20 21 17 2 19 15 22 18 3 20 20 17 19 4 24 21 16 23 5 22 19 21 21 Average Number of Defects Daily per Machine Operator A B C D 1 0.3 0.9 0.6 0.4 2 0.8 0.5 1.1 0.7 3 1.1 1.3 0.6 0.8 4 1.2 0.8 0.6 0.9 5 1.0 0.9 1.0 1.0 The company wants to determine which operator to assign to each…Easyville University awarded scholarships of $50,000.00 each to two students for a bachelor’s degree program. The standard time for degree completion is four years or 8 semesters. Easyville University stipulates that the scholarship amount will be increased or decreased depending on how well the students meet, exceed or fail to meet the standard time (i.e. more money for exceeding standard and less for failing to meet standard). Sam Speedy completed his degree program in three and one half years; while Larry Laggard completed his degree program in five years. Using the Standard Hour Plan, how much scholarship money will be given to: a)Speedy Sam? b) Larry Laggard?Saad has been a manager at Revel Consulting for the past five years. As the business has grown, Saad has taken on more and more responsibilities and is now at the point where he is working on over 10 projects every quarter. Saad’s supervisor, Vance, wants Saad to hire two assistant managers to aid Saad in managing projects; however, while Saad agrees that he is becoming overwhelmed, he fears that additional employees will make completing the projects more difficult, which makes him hesitant to agree with Vance’s plan. Saad appears to be stuck at which step of the motivational process? a. Need b. Motive c. Satisfaction or dissatisfaction d. Feedback 4.Which theory holds that needs are based on personality and are developed and learned as people interact with the environment? a. Acquired needs theory b. Hierarchy of needs theory
- 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…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 $8000. 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 region.…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 $8000. 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