Plant Electronics Limited is considering producing three new computer boards on a daily basis. Each board will be produced from various combinations of plastic, copper and transistors. The amount of each resources required per unit, the unit profitability, and the availability of the resources are summarized in the following table: Chip Plastic Copper Transistors Profit per model unit GH¢ Х12 1 1 4 T7 1 2 1 1.5 V8 1 1 1 3 Daily 80 80 70 availability (a) Formulate the linear programming problem to determine the production levels for three models X12, T7 and V8 that will maximize profit. (b) Use solver to find optimal solution and sensitivity report.

Plant Electronics Limited is considering producing three new computer boards on a daily basis. Each board will be produced from various combinations of plastic, copper and transistors. The amount of each resources required per unit, the unit profitability, and the availability of the resources are summarized in the following table: Chip Plastic Copper Transistors Profit per model unit GH¢ Х12 1 1 4 T7 1 2 1 1.5 V8 1 1 1 3 Daily 80 80 70 availability (a) Formulate the linear programming problem to determine the production levels for three models X12, T7 and V8 that will maximize profit. (b) Use solver to find optimal solution and sensitivity report.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...

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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 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.
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