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QUESTION TEN a) Explain the value of sensitivity analysis in linear programming problems and show how dual values are useful in identifying the price worth paying to relax constraints. b) J.A Computers is a small manufacturer of personal computers. It concentrates on production of three models- a Desktop 386, a Desktop 286, and a Laptop 486, each containing one CPU Chip. Due to its limited assembly facilities JA Computers are unable to produce more than 500 desktop models or more than 250 Laptop models per month. It has one hundred and twenty 80386 chips (these are used in Desktop-386) and four hundred 80286 chips (used in desktop 286 and Laptop 486) for the month. The Revision Questions and Answers 23 Desktop 386 model requires five hours of production time, the Desktop 286 model requires four hours of production time, and the Laptop 486 requires three hours of production time. J.A Computers have 2000 hours of production time available for the coming month. The company estimates that the profit on Desktop 386 is Sh. 5,000. for a desktop 286 the profit is Sh.3,400 and Sh.3,000 profit for a laptop 486. Required: Formulate this problem as a profit maximization problem and mention the basic assumptions that are inherent in such models. C) An extract of the output from a computer package for this problem is given below: Output solution X1=120, X2=200, X3=200 Dual values Constraints 3 Constraints 4 90 Constraints 5 20 Sensitivity analysis of objective function coefficients: Variable Lower Original Upper limit value imit 100 250 No limit 150 170 200 27.5 150 170 Sensitivity analysis on R.H.S ranges. Constraint Lower Original Upper limit value limit 320 500 No limit 200 250 No limit A W N 80 120 130 350 400 412.5 5 1950 2000 2180 X1=Monthly production level for Desktop 386. Xa =Monthly production level for Desktop 286. Xy=Monthly production level for Laptop 486. Required: 1 ) Interpret the output clearly, including optimum product mix, monthly profit, unused resources and dual values Explain the purpose of upper limits and lower limits for the variables X1,X2,Xy and constraints 1 to 5. in) Calculate the increase in profit if the company is able to produce a further 10 CPU 80386 chips. (Q 7 July 2000 Pilot paper) QUESTION ELEVEN a) Explain the following terms as used in the context of linear programming. 1) Linear program ii) Basic feasible solution Degeneracy iv) Alternative optimal solutions v ) Redundant constraints vi) Range of optimality vii) Artificial variables vili) Reduced cost ix) Dummy destination *) Assignment