A construction company has an opportunity to build some shopping malls during the next year. The expected net profit and expected cost for each of the shopping malls are shown in the table below:

Shopping Mall	Expected Net Profit (in $1000)	Expected Net Cost (in $1000)
1	200	150
2	150	90
3	140	50
4	125	80
5	180	100

The company has budget $300,000 for the construction of shopping malls during the next year. Each mall can only be built at most once. Also, due to various legal restrictions and marketing considerations, the following relationships among the projects must be met:

1. Exactly one of three shopping malls, 1, 2 and 5 must be constructed.
2. At most one of the two shopping malls 1 and 4 may be constructed.
3. If shopping mall 4 is constructed, then shopping mall 2 also must be constructed, and vice versa.
4. If shopping mall 1 is selected, then shopping mall 2 and 3 must be constructed.

Formulate this problem to determine the best set of shopping malls the company should build to maximize the total net profit. algebraically formulate this problem