# Model 8: Summer Job

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 $5,000.
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 were looking for an interesting summer job anyway (maximum of 600
hours), you have decided to participate in one or both friends ventures in
which combination would maximize your total estimated profit. You now need
to solve the problem of finding the best combination.

Decision Variables: P_{i} = percent participation in project i=1,2

Objective: Maximize Profit= 4500 P_{1} + 5000P_{2}

Constraints:

Budget: 5000P_{1} + 4000P_{2} <= 6000

Time: 400P_{1} + 500P_{2} <= 600

Percents: 0<= P_{1} <= 1, 0<= P_{2} <= 1