the fairwinds development corporation is considering taking part in one or more different development projectsa b and cthat are about to be launched each project requires a 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 year project a project b project c 1 8 9 13 2 10 10 10 3 12 7 9 4 40 9 9 5 0 46 7 6 0 0 62 fairwinds has 18 million cash on hand now and also expects to receive 8 million in other income at the start of each year year 1 through year 6 that would also be available for investments therefore a total of 26 million is available for projects in year 1 assume that money not spent in a given year is available in future years and also earns 1 interest for example if the ending balance in year 1 is 1 million then 101 million will be available for projects at the start of year 2 along with the 8 million from other income for year 2 assume no interest earned for year 1 as it is already included in the 18 million starting balance for simplicity you may assume that all cash flows including interest earned other income received and project cash flows occur simultaneously at the start of each year the company may participate in each project either fully fractionally with other development partners or not at all if fairwinds participates at less than 100 then all the cash flows associated with that project are reduced proportionally for example if fairwinds participates in project a at 50 the cash flows associated with that project would be 4 5 6 and 20 million in years 1 through 4 respectively company policy requires ending each year with a cash balance of at least 700 thousand interest is earned on all remaining cash including the 700 thousand minimum balance which projects should fairwinds take part in and at what fraction of participation so as to end year 6 with as much cash as possible formulate and solve a linear programming spreadsheet model