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?
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