Suppose that you have recently been hired to help manage a companys pension fund. The funds required to make the payments on the first day of each year for the period 2007-2021 are shown in the Problem 2worksheet. Assume that you are going to finance these payments by buying bonds. Three type of bonds (bond 1, bond 2, and bond 3) areavailable for purchase on January 1, 2007. The price (cash outflow) and coupons (cash inflows) for one unit of each bond are also provided in the Problem 2worksheet. Assume that all coupon payments are received on January 1 and arrive in time to meet the cash demands for the date on which they arrive. On January 1, 2007, you purchase bonds and then meet your first required payment of $15,000. During each year the excess cash on hand earns 3% interest. Using a linear programming model, determine the number of each bond that should be purchased in order to minimize the January 1, 2007 investment needed to meet the 2007-2021 cash requirements. You may assume that fractional numbers of bonds can be purchased.

Problem 2
	2007	2008
Required payment at start of year	$15,000	$16,000
Cash outflows (in 2007) and inflows (in other years) from one unit of each bond
	2007	2008
Bond 1	($980)	$60
Bond 2	($970)	$65
Bond 3	($1,050)	$75
Annual interest rate	3%
Number of bonds (allowing fractional values) to purchase in 2007
Bond 1
Bond 2
Bond 3
Money allocated to buy bonds and cover 2007 payment
Constraints to meet payments
	2007	2008
Amount available
Amount required	$15,000	$16,000
Amount to allocate in 2007	$0.00

Please show all formulas in excel, thank you.