1. How a management science technique can be used as adecision support system?State your analysisand provides some examples.
2. Amanufacturingcompanymakestwomodels A and B of a product. Each piece of Model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of Model B requires 12 labour hours for fabricatingand3labourhoursforfinishing.Forfabricatingandfinishing,themaximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs8000oneachpieceofmodelAandRs12000oneachpieceofModelB.Howmany piecesofModelAandModelBshouldbemanufacturedperweektorealiseamaximum profit? What is the maximum profit perweek?

Totalprofit(inRs)=8000x+12000y

LetZ = 8000x+ 12000y

We now have the following mathematical model for the given problem.

Maximise Z = 8000x+12000y

subject to the constraints:

9x+ 12y180

x+ 3y30

x?/0,y/>0

3.Referring to Question 4, the coefficient function ofZ = 8000 x + 12000yis changed toZ= 10000 x + 12000y.State your analysis by explaining what is a sensitivity analysis and the effect of its coefficient changing

4. A manufacturing company makes two models A and B of a product. Each piece of Model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of Model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs 8000 on each piece of model A and Rs 12000 on each piece of Model B. How many pieces of Model A and Model B should be manufactured per week to realise, a maximum profit? What is the maximum profit per week? Total profit (in Rs) = 8000 x + 12000 y Let Z = 8000 x + 12000 y We now have the following mathematical model for the given problem. Maximise Z = 8000 x + 12000 y subject to the constraints: 9r + 12y s 180 x+ 3y $ 30 x20,1 20 5. Referring to Question 4, the coefficient function of Z = 8000 x + 12000y is changed to Z= 10000 x + 12000y. State your analysis by explaining what is a sensitivity analysis and the effect of its coefficient changing