1. Wilkinson Auto Dealership is contemplating selling one or more of the following types of automobiles—sedans, SUV’s, and trucks. There is a fixed license fee per year for doing business in each line, $100,000, $250,000, and $50,000, respectively. The profit contribution exclusive to the fixed cost is $250.00 per unit for sedans, $700.00 per unit for SUV’s, and $150.00 per unit for trucks. The company is planning the placement of orders with the manufacturer for next year. Dealer preparation takes 2 hrs/sedan, 3.0 hrs/SUV, and 1.5 hrs/truck. They have 4400 hrs of preparation time next year. Sedans take 1 unit of space, SUV’s take 1.5 units of space, and trucks take 1.1 units of space. 1200 units of space are available. How many sedans, SUV’s, and trucks should be ordered in order to maximize total profit contribution less fixed costs incurred? Define the decision variables, constraints, and the objective function for this problem. (Allow the order quantities to be fractional).
2. You have to solve a Traveling Salesperson problem. Select 30 visiting points around your regular life and determine distance matrix through Internet map services such as Google and Naver. Then solve it to minimize total traveling distance of the salesperson by using the LINGO program given to you. After solution, you have to check total solution time and the CPU speed and RAM size of computer which you used to solve this question (set LINGO à Option àGlobal Solver àcheck using Global solver).
3. Market research corporation of Toledo Inc. (MRCT) has to finalize recommendation for the 2015 advertising campaign for Miracle Motors Inc. (MM), a major hydrogen-powered automobile manufacturer. MRCT has developed 5 distinct campaigns for MM Inc. MM Inc. has 7 distinct customer segments, and it wants all of its customers to be “hit” by at least one of its campaigns. It wants to minimize the total cost of reaching its customer base through these campaigns. Formulate this problem and solve it by using Lingo.
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