Problem $3.(15$ 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.

This problem is an example of

$\_$ problems. Given a set of items,

each with a weight and a value, determine the number of each item to include in a collection

$($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.

At most two of investments $1-4$ can be selected.

At least one of investments $5-7$ must be selected.

If investment $3$ is selected, at least one of investments $1-2$ must be selected.

To select both investments $1$ and $2,$ investment $3$ must be selected.