Khadija Textile Mills produces two types of cottoncloth—Roughand Smooth. Smooth is a heavier grade of cotton cloth and, as such,requires 7.5 kg of raw cotton per meter, whereas Rough requires 5kg of raw cotton per meter. A meter of Smooth requires 3.2 hours ofprocessing time; a meter of Rough requires 3.0 hours. Although thedemand for Rough is practically unlimited, the maximum demand forSmooth is 510 meters per month. The manufacturer has 6,500 kg ofcotton and 3,000 hours of processing time available each month. Themanufacturer makes a profit of OMR2.25 per meter of Rough andOMR3.10 per meter of Smooth. The manufacturer wants to know howmany meters of each type of cloth to produce to maximizeprofit.?
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 meterof Rough is increased from OMR2.25 to OMR3.00?
4.Solve the linear programming model for Khadija Textile Mills byusing the computer. Produce the solution and tell if KhadijaTextile Mills can obtain additional cotton or processing time, butnot both, which should it select? How much? Explain youranswer.
5.Identify the sensitivity ranges for the objective functioncoefficients and for the constraint quantity values. Then explainthe sensitivity range for the demand for Smooth.
