Khadija Textile Mills produces two types of cotton cloth-Rough and Smooth. Smooth is a heavier grade...

 

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Khadija Textile Mills produces two types of cotton cloth-Rough and Smooth. Smooth is a heavier grade of cotton cloth and, as such, requires 7.5 kg of raw cotton per meter, whereas Rough requires 5 kg of raw cotton per meter. A meter of Smooth requires 3.2 hours of processing time; a meter of Rough requires 3.0 hours. Although the demand for Rough is practically unlimited, the maximum demand for Smooth is 510 meters per month. The manufacturer has 6,500 kg of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of OMR2.25 per meter of Rough and OMR3.10 per meter of Smooth. The manufacturer wants to know how many meters of each type of cloth to produce to maximize profit. Answer the following questions: (2 Marks each) 1. Formulate a linear programming model for this problem. 2. Solve the model graphically and explain the solution. 3. What is the effect on the optimal solution if the profit per meter of Rough is increased from OMR2.25 to OMR3.00? 4. Solve the linear programming model for Khadija Textile Mills by using the computer. Produce the solution and tell if Khadija Textile Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer. 5. Identify the sensitivity ranges for the objective function coefficients and for the constraint quantity values. Then explain the sensitivity range for the demand for Smooth. Khadija Textile Mills produces two types of cotton cloth-Rough and Smooth. Smooth is a heavier grade of cotton cloth and, as such, requires 7.5 kg of raw cotton per meter, whereas Rough requires 5 kg of raw cotton per meter. A meter of Smooth requires 3.2 hours of processing time; a meter of Rough requires 3.0 hours. Although the demand for Rough is practically unlimited, the maximum demand for Smooth is 510 meters per month. The manufacturer has 6,500 kg of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of OMR2.25 per meter of Rough and OMR3.10 per meter of Smooth. The manufacturer wants to know how many meters of each type of cloth to produce to maximize profit. Answer the following questions: (2 Marks each) 1. Formulate a linear programming model for this problem. 2. Solve the model graphically and explain the solution. 3. What is the effect on the optimal solution if the profit per meter of Rough is increased from OMR2.25 to OMR3.00? 4. Solve the linear programming model for Khadija Textile Mills by using the computer. Produce the solution and tell if Khadija Textile Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer. 5. Identify the sensitivity ranges for the objective function coefficients and for the constraint quantity values. Then explain the sensitivity range for the demand for Smooth.

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