Mathematically formulate an algebraic model for the problem in compact notation (using summation notation). The problem is to maximize total profit by selecting investment opportunities. Clearly define the decision variables and the indexes, the notation for the parameters, and then use decision variables, parameter notations, and summations to come up with the compact formulation.

E*7.6. The board of directors of General Wheels Co. is con- sidering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the fol- lowing table. Investment Opportunity 1 2 3 4 5 6 7 Estimated Profit Capital Required (millions) (millions) $17 $43 10 28 15 34 19 48 7 17 13 32 9 23 mund The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is under- taken. There are no such restrictions on investment opportunities 5, 6, and 7. The objective is to select the combination of capi- tal investments that will maximize the total estimated long-run profit (net present value)