lem 3. (15 pts) Integer Programming Model A company is considering seven investments. The initial cash outflow (cost) and net present value (yield) for each investment are given below. The cash available for investment is $13,000. Note that if the company wishes to take part in any of these investments, it must "go all the way." In other words, partial investments are not permitted. Cash Required NPV Added Investment 1 $5,000 $16,000 Investment 2 $2,500 $8,000 Investment 3 $3,500 $10,000 Investment 4 $6,000 $20,000 Investment 5 $7,000 $22,000 Investment 6 $4,500 $12,000 Investment 7 $3,000 $8,000 1. This problem is an example of each with a weight and a value, determine the number of each item to include in a collection problems. Given a set of items, (typically either 0 or 1) so that the total weight is less than a given limit and the total value is as large as possible. For each of the following logical restrictions, please write the constraint necessary to model the restriction within this problem. 2. At most two of investments 1-4 can be selected. 3. At least one of investments 5-7 must be selected. 3. At least one of investments 5-7 must be selected. 4. If investment 3 is selected, at least one of investments 1-2 must be selected. 5. To select both investments 1 and 2, investment 3 must be selected