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Suppose you have just inherited $6,000 and you want to invest it. Upon hearing this news, two different friends have offered you an opportunity to become a partner in two different entrepreneurial ventures, one planned by each friend. In both cases, this investment would involve expending some of your time next summer as well as putting up cash. Becoming a full partner in the first friend's venture would require an investment of $5,000 and 400 hours, and your estimated profit (ignoring the value of your time) would be $4,500. The corresponding figures for the second friend's venture are $4,000 and 500 hours, with an estimated profit to you of $4,500. However, both friends are flexible and would allow you to come in at any fraction of a full partnership you would like; your share of the profit would be proportional to this fraction.
Because you are looking for an interesting summer job anyway (maximum of 600 hours), you have decided to participate in one or both friends' ventures. Which conbination would maximize your total estimate profit? You now need to solve the problem to find the best combination.
1) Formulate the linear programming model for this problem
2) Solve this model graphically. What is your total estimated profit?
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