This is your lucky day. You have just won a $10,000 prize. You are setting aside $4,000 for taxes and partying expenses, but you have decided to invest the other $6,000. 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. Become full member 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. If you choose a fraction of a full partnership, all the above figures given for a full partnership (money investment, time investment, and your profit) would be multiplied by this same 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 whichever combination would maximize your total estimated profit. You now need to solve the problem of finding the best combination.

a) Describe the analogy between this problem and the RMC problem discussed in class. Then construct a table and fill in the data, identifying the activities to be done, resources, resource usage per unit of activity, amount of resource available, unit profits, etc.
b) Identify verbally the decisions to be made, the constraints on these decisions, and the overall measure of performance (objective function) for the decisions.
c) Convert these verbal descriptions of the constraints and the measure of performance into quantitative expressions in terms of the data and decisions. In other words, formulate the model algebraically by defining the decision variables and writing the constraints and the objective function.
d) Use the graphical solution method to solve this model. What is the optimal solution and the total estimated profit?
e) Set up an (Excel) spreadsheet model and use the Excel Solver to solve the model and verify the solution the solution you found in part (d)