A company produces bicycle frames using two fibreglass materials that improve the strength-to-weight ratio of the frames. The cost of standard grade material is Rs 750 per yard and the cost of professional grade material is Rs 900 per yard. The standard and professional grade materials contain two different amounts of fibreglass, carbon fibre and Kevlar as given in table Standard Grade Professional Grade Fibre Glass 84% 58% Carbon Fibre 10% 30% Kevlar 6% 12% The company signed a contract with a bicycle manufacturer to produce a new frame with a carbon fibre content of at least 20 percent and Kevlar content of not more than 10 percent. To meet the required weight specification, a total of 30 yárds of material must be used for each frame. (i)Formulate an LPP to determine the size of each grade of fibreglass materials that the company should use in each frame to minimise the total cost. Use graphical method. (ii)If the company is offered professional grade at Rs 800 per yard, will the optimal solution change? What effect will the further lowering of price have on the optimal solution?

A company produces bicycle frames using two fibreglass materials that improve the strength-to-weight ratio of the frames. The cost of standard grade material is Rs 750 per yard and the cost of professional grade material is Rs 900 per yard. The standard and professional grade materials contain two different amounts of fibreglass, carbon fibre and Kevlar as given in table Standard Grade Professional Grade Fibre Glass 84% 58% Carbon Fibre 10% 30% Kevlar 6% 12% The company signed a contract with a bicycle manufacturer to produce a new frame with a carbon fibre content of at least 20 percent and Kevlar content of not more than 10 percent. To meet the required weight specification, a total of 30 yárds of material must be used for each frame. (i)Formulate an LPP to determine the size of each grade of fibreglass materials that the company should use in each frame to minimise the total cost. Use graphical method. (ii)If the company is offered professional grade at Rs 800 per yard, will the optimal solution change? What effect will the further lowering of price have on the optimal solution?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 35P

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Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
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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