2) (10 marks) A local transportation company decided to offer direct service from Whistler to downtown Vancouver. Management must decide between a full-price service using the company's new fleet of full capacity bus and a discount service using smaller capacity vans. The best choice depends on the market reaction to the service they offer. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to downtown Vancouver: strong and weak. The following table shows the estimated monthly profits (in dollars): Demand for service Strong Weak Service Full Price 360 -70 Discount 190 -10 a) If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, approach? (2 marks) b) Suppose that management of this local transportation company believes that the probability of strong demand is 0.6 and the probability of weak demand is 0.4. Use the expected value approach to determine the optimal decision. (5 marks) c) What is the expected value of the perfect information? (3 marks) 3) (20 marks) Answer the following questions using the sensitivity report shown below: a) Report the optimal solution and the optimal value of the objective function. (6 marks) b) Calculate the amounts of slack/surplus and comment on what constraints are binding and which ones are non-binding (6 marks) c) How much improvement in the objective function will we get if we increase the amount of Steel by 12 more units? (3 marks) d) Calculate the optimal value of the objective function (according to this sensitivity report) if the coefficient of x changes to 8 and the coefficient of y changes to 7 simultaneously. Show all of the calculations (5 marks) Variable Cells Allowable Final Reduced Objective Allowable Decrease Cell Value Cost Coefficient Increase Type 4 3 0 6 3 A Type 3 4 0 5 B Type 1E+30 0 -4.5 3.5 с Allowable Allowable Decrease Increase 6 20 10 5 Name X y Z Constraints Name 2 3 Cell Wood Steel hours Final Value 32 30 15 Shadow Price 1.5 0 2.5 4 3 Constraint R.H. Side 32 40 15 15 10
