Problem 1 [ 5 marks] Company, which manufactures makes hockey sticks and chess sets.Each hockey stick yields an incremental profit of $5, and each chess set, $5. - A hockey stick requires 6 hours of processing at Machine Center A and two hours at Machine Center B. A chess set requires 6 hours at Machine CenterA, 8 hours at Machine Center B, and 2 hours at MachineCenter C. - Machine Center A has a maximum of 60 hours of available capacity per day, Machine Center B has 36 hours, and Machine Center C has 10 hours. If the company wishes to maximize profit, how many hockey sticks and chess sets should be produced per day? Answer the following: a) Formulate the linear programming model to determine the optimal solution b) Use Excel solver to generate the sensitivity report and Interpret the sensitivity report. c) Use Solvertable to investigate further the sensitivity of the various input (discuss) 1Problem 2 [ 5 marks] L.P. : Scheduling Problem A commercial Airline in the UAE has 4 flight attendants that it wants to assign 4 monthly schedules in a way to minimize the number of nights they will be away from home. The numbers of night each attendant must be away from home with each schedule is given in the following table: Identify the optimal scheduling in order to minimize the total number of nights the attendants will be away from home Problem 3 [ 5 marks] For a given business the cost of an emergency generator is $400,000. In case it is installed there is no loss from power failure. There is 14% chance of power failure. In case there is power failure there is a probability of 0.06 that the loss would be $35 millions. And there is probability of 0.94 that the loss would be only $600,000. Determine whether the business should build the emergency generator. Use treePlan to check your answer. Problem 4 [ 5 +5 =10 marks] Suppose you have three options to start a business near a good mall that attracts students: Opening a medium-sized shop, or a small shop or no shop at all. The market can be good, average or bad. The probabilities for these three possibilities are 0.2 for a good market, 0.5 for an average market, and 0.3 for a bad market. The net profit or loss for the three business options are given in the following table. Part A a) Construct a decision tree for this problem. b) If the decision maker knows nothing about the probabilities of the states of nature, find the recommended decision and the corresponding profit using: b1) Optimistic approach b2) Conservative approach Scheduling Attendant Schedule A Schedule B Schedule C ScheduleAlternative Good Market Average Market Bad Market Small shop 75,000 25,000 -40,000 Medium size shop 100,000 35,000 -60,000 No shop 0 0 0 2b3) Minimax regret approach c) Suppose that the decision maker obtained the probabilities P(good market) = 0.2, P(average market)=.50, and P(bad market)=0.3, c.1) What is the recommended decision using the expected value approach? (explain). c.2) What is the optimal decision(s) if perfect information were available? What is the expected value of perfect information? Interpret it. [ optimal decision(s) if perfect information were available, EVwPI( Expected value with Perfect Information, EVPI ( Expected value of perfect information] d) Carry the sensitivity analysis describing how changes in the state-of-nature probabilities affect the recommended decision alter