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5 Pages Essays / Projects Year: Pre-2021

Question 1: Sydney Cargo has to decide on the purchasing policy of new aircrafts. Three different aircrafts are offered to the company: large aircrafts, medium aircrafts and small aircrafts. The available purchasing budget is 120 million dollars. The purchasing costs are 8 million dollars for a large aircraft, 5 million dollars for a medium aircraft and 2 million dollars for a small aircraft. The company employs 30 pilots and each aircraft is flown by a single pilot. Assuming that only small aircrafts are purchased, the technical department can service 60 aircrafts each month. Servicing a medium aircraft requires an additional 50% effort, and servicing a large aircraft requires 2.5 times the effort of servicing a small aircraft. The capacity of the aircrafts is measured in tonne-mile units. Large aircrafts have a monthly capacity of 450,000 tonne-miles, medium aircrafts a capacity of 200,000 tonne-miles and small aircrafts a capacity of 80,000 tonne-miles. The company’s revenue is 20 cents per tonne-mile. The total monthly demand is estimated to be 7 million tonne-miles (note that the company is not required to meet demand.). The fixed costs of operating the aircrafts are $70,000, $30,000 and $10,000 for large, medium and small aircrafts, respectively. The company’s goal is to maximize the monthly profits. (Note that the purchasing budget does not play a role in the monthly profit.) 1. Formulate as an LP model. 2. Solve the problem using the Excel Solver. What is the optimal purchasing policy and what is the profit under this policy? (Provide a screenshot of your Excel solution!) Question 2: You are given the following LP problem: MaxCx1


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