1.Consider the linear programming model (given in the Par- tial Answers to Selected Problems in the back of the book) that was formulated for Prob. 3.2-3. (a) Use graphical analysis to identify all the corner-point solutions for this model. Label each as either feasible or infeasible. (b) Calculate the value of the objective function for each of the CPF solutions. Use this information to identify an optimal solution. (c) Use the solution concepts of the simplex method given in Sec. 4.1 to identify which sequence of CPF solutions might be examined by the simplex method to reach an optimal solution. (Hint: There are two alternative sequences to be identified for this particular model.)

3.2-3)This is your lucky day. You have just won a $20,000 prize. You are setting aside $8,000 for taxes and partying expenses, but you have decided to invest the other $12,000. Upon hearing this news, two different friends have offered you an opportunity to be- come a partner in two different entrepreneurial ventures, one planned by each friend. In both cases, this investment would in- volve expending some of your time next summer as well as putting up cash. Becoming a full partner in the first friends venture would require an investment of $10,000 and 400 hours, and your esti- mated profit (ignoring the value of your time) would be $9,000. The corresponding figures for the second friends venture are $8,000 and 500 hours, with an estimated profit to you of $9,000. 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 any- way (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 Wyndor Glass Co. problem discussed in Sec. 3.1. Then construct and fill in a table like Table 3.1 for this problem, identifying both the activities and the resources. (b) Formulate a linear programming model for this problem. D,I (c) Use the graphical method to solve this model. What is your total estimated profit?