just solve problem 2

Problem 1: Littlewoods Rule (10 points) A newly created AirRarotonga flight from Rarotonga to Aitutaki has 20 seats. The high fare on the flight is $800 and the restricted/low fare is $300. There is ample demand for the low fare class, but high fare demand is random. Further, the customers who buy low fares buy their tickets well in advance before high fare customers. Assume the demand d for the high fare is distributed according to the following discrete probability distribution: 16 demand al 0 21 31 Probid 0.005 0.005 0.01 0.05 51 0.11 61 02 011 71 81 91 10 11 12131 14 151 0.2 0.15 0.05 0.04 0.03 0.02 0.015 0,015 0.01 When answering the following questions, show your calculations. a. Mr. Wright is in charge of the flight booking operations and decides to set a protection level for the high fare. What is the optimal protection level for the high fare? (2 points) b. Suppose a protection level of 8 is chosen. How many high fare passengers does the airline expect to turn away due to a lack of capacity? (2 points) c. Suppose a protection level of 8 is chosen. How many seats are expectedly empty at departure? (2 points) d. Assuming a protection level of 8, what is the total expected revenue for low and high fare passengers? Write down your analytical calculation. (2 points) e. Suggest two reasonable extensions to the optimization model that is underlying Littlewood's rule and motivate your suggestion. What challenges do you expect with these extensions? (2 points) Problem 2: Multi-resource Capacity Allocation (10 points) Assume you are the Revenue Manager at the retailer Mega Market. You want to optimize the product assortment in your store. You use the well-known deterministic linear programming (DLP) approach for capacity control for a specific sales day. Max {p,; s. t. X y,V; 5G (I = 1.,m),0 s y, SE(0) 6= 1.,n) Please answer the following questions with 1-2 sentences cach (1 point cach). a. In the context of this example, how would you interpret product j in the above model? b. In the context of this example, what is the meaning of the decision variables? c. In the context of this example, please explain the objective function. d. In the context of this example, please explain the capacity constraints. What is the meaning of a resource ! ? e. Is the objective function concave? Why or why not? f. Name two critical assumptions underlying the model. g. How does the objective function change if demand is modelled as a random variable with known probability distribution? Write down the objective function. h. How can you obtain bid prices from the DLP? i. Assume that in the optimal solution, there is a resource I that with a total capacity utilization of expectedly 90%. What is the optimal bid price for this resource? j. Bid prices can be obtained, among other approaches, from the DLP or the randomized linear program (RLP). Which one of the two will yield higher revenues in general