1. Jerry owns six assets that he must sell over the next three years. He expects that the sales will generate the following revenue, in millions of $

	Year 1	Year 2	Year 3
Asset 1	15	20	24
Asset 2	16	18	21
Asset 3	22	30	26
Asset 4	10	20	30
Asset 5	17	19	22
Asset 6	19	25	29

For example, if he sells asset 3 in year 2, he receives $30 million. Each asset can be sold at most once, of course. He must sell at least $20 million of assets in year 1, $30 million in year 2, and $35 million in year 3.

Formulate and solve this Integer Program with Binary variable. How can he maximize his total revenue from the sales? What is the maximum revenue?

2. XYZ Manufacturing must produce 1650 units for an important customer. If machine 1 is used its production will be between 300 and 1500 units. Machine 2 and/or machine 3 can be used only if machine 1’s production is at least 1000 units. Machine 4 can be used with no restrictions. The following table provides the fixed and variable (per unit production) cost of production at each machine type as well as the minimum and maximum allowed production limits of each machine. If a machine is used, its fixed cost is incurred.

Fixed               Variable          Minimum        Maximum

Machine          Cost($)            Cost($)            Production      Production

1                      500                 2.00                 300                  1500

2                      800                 0.50                500                  1200

3                      200                  3.00                 100                  800

4                      50                    5.00                 no limit           no limit

Formulate a mixed-binary linear programming model to help XYZ managers to determine production quantities on the machines to minimize costs. No need to solve.