1. Kings Auto has three plants in Los Angeles, Detroit, and New Orleans, and two major distribution centers in Denver and Miami. The following table shows the demands for distribution centers, capacities for plants and the mileages between plants and distribution centers. Denver Miami Capacities Los Angeles 1000 miles 2690 1000 Detroit 1250 1350 1500 New Orleans 1275 850 1200 Demand 2300 1400 The trucking company in charge of transporting the cars charges 8 cents per mile per car. a) Formulate this transportation problem as LP model. Use Lindo to get the minimum transportation cost. b) Solve this problem using the transportation algorithm. Make sure that the solutions for both a) and b) are the same. 2. A business executive must make the four round trips between the head office in Dallas and a branch office in Atlanta. Departure date from Dallas Return date to Dallas Monday, July 6 Friday, July 10 Monday, July 13 Wednesday, July 15 Monday, July 20 Friday, July 24 Tuesday, July 28 Friday, July 31 The price for a round ticket from Dallas is $400. A discount of 25% is granted if the dates of arrival and departure of a ticket span a weekend (Saturday and Sunday). If the stay in Atlanta lasts more than 21 days, the discount is increased to 30%. A one-way ticket between Dallas and Atlanta (either direction) costs $250. How should the executive purchase the tickets? a) Set up this problem as an assignment problem and formulate this problem as LP model. b) Describe the plan for the trips. Hint: Use the code (city, date) to define the rows and columns of the assignment problem. For example: the assignment (D, 6) – (A, 10) means leaving Dallas on July 6 and returning from Atlanta July 10 at a cost of $400. Please complete the following table then solve this problem as an assignment problem. (A,10) (A,31) (D, 6) $400 300 300 400 300 300 300 (D, 28) 3. In a gas station there is one gas pump. Cars arrive at the gas station according to a Poisson process. The arrival rate is 20 cars per hour. Cars are served in order of arrival. The service time (i.e. the time needed for pumping and paying) is exponentially distributed. The mean service time is 2 minutes. Answer the following questions. Don’t need to solve this problem by hand and run a model using QTS Plus to answer the followings. a) Once you arrived at the gas station for gas, what is the expected number of cars in the waiting line? b) How long does it take to get served (unit in minutes)? c) Is it worth to install another pump? Assume that no additional information was given. Answer with the QTS Plus output.