Problem 2. You plan to sell k products to totally n1 + n2 customers in which customers 1, ...,n1 are from Town 1 and customers n, + 1, … ,n1 + n2 are from Town 2. In addition, as the products are very expensive, two customers will co-buy one produce, each getting 50% of the ownership. Due to ... transportation reason, for each product, you have to sell it to two customers from the same town. It is also assumed that each customer can buy at most three products (each with 50% of the ownership) and that each product must be sold to exactly two customers. Let c¡¡ be the price that customer i offers for his/her 50% of the ownership for product j (i = 1, -,n1 + n2;j = 1, , k). Formulate the problem to %3D maximize your total revenue. Clearly define all the decision variables in the beginning of your solution. [Hint: use one variable to denote the customer (selling product j to customer i ?) and another variable to denote the town (selling product j to Town 1?)]

Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,600. Manufacturing costs are $14 for each 4-cylinder connecting rod and $19 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,000 6-cylinder connecting rods and 7,000 4-cylinder connecting rods. Let 56 = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise (a) Using the decision variables x4 and s, write a constraint that limits next…

23) Max and Jill both uses quarters to fill a parking meter. Max's parking meter is for 2 hours and Jill's parking meter is for 1 hour and 30 minutes. Max goes into a store and when he comes back, he sees that his parking meter has 4 of the time left. Jill goes for a run and when she comes back she sees that her parking meter has 4 of the time left. Who has more time left? By how many minutes?

A twenty-something single person is planning a ski vacation. Assume that he has 2 possible destinations: Utah, and Oregon. There are 4 ski areas in Utah with 4 available times for 3 of the areas, and 1 times for the other area. There are 4 ski areas in Oregon with 2 available times for 3 of the areas, and 4 times for the other area. (A "time" refers to a weekend for which there are vacancies at the ski lodge.) A trip plan involves the selection of a location, ski area, and a time. How many possible plans are there?