Brown Brother Construction is considering four residential development projects: The Evergreen, English Hill, Kempton Meadow, and Grey Stone. Each development project requires significant investment over the next few years and then would be sold upon completion. The projected cash flows (in millions of dollars) associated with each project are shown in the table below

Brown Brother Construction starts with $14 million cash on hand and also expects to receive $6 million in other income at the start of each year (1 through 5). Thus, a total of $20 million will be available for investment at the start of year 1. Assume that money not spent in a given year is available in future years, and also earns 2% interest. For example, if the ending balance in year 1 is $1 million, then $1.02 million will be available for projects in year 2 (along with the $6 million in other income for year 2). Assume no interest earned for the beginning of year 1 as it is already included in the $14 million starting balance. Assume that all cash flows occur simultaneously at the start of each year (e.g., income in a given year can be used for investment in that same year).

Year Evergreen English Hill Kempton Meadow Grey Stone

1 -12 -4 -6 -9

2 -8 -4 -7 -8

3 -10 -7 17 -7

4 -4 26 0 -7

5 44 0 0 38

By acting now, the company may participate in each project either fully, fractionally (with other development partners), or not at all. If the company participates at less than 100%, then all the cash flows associated with that project are reduced proportionally. For example, if the company participates in The Evergreen at 50%, the cash flows associated with that project would be -6, -4, -5, -2, and $22 million at the start of years 1 through 5, respectively. Company policy requires ending each year with a cash balance of at least $1 million. (Interest is earned on all remaining cash, including the $1 million minimum balance.) Which projects should Brown Brother Construction take part in and at what fraction of participation, so as to end year 5 with as much cash as possible? Formulate and solve a linear programming spreadsheet model.