Homework $5(18$pts$).$ Due by $11$:$59$pm$,$ Sunday, April $14.$

Problem $1.(8$pts$)$ You must choose among a set of projects $($each project is unique and cannot be repeated$).$ The net present value of the future stream of returns, as well as the capital requirements for the next three years are given below. The available capital funds for the next three years are: $$7,000$ for Year $1,$$$5,000$ for Year $2,$ and $$6,000$ for Year $3.$ If you wish to maximize net present value, what projects should you take on$?$

$\backslash$table$[[$Project $($i$),\backslash$table$[[$Net present$],[$value $($$$)]],\backslash$table$[[$Capital$],[$requirements for$],[$Year $1($$$)]],\backslash$table$[[$Capital$],[$requirements for$],[$Year $2($$$)]],\backslash$table$[[$Capital$],[$requirements for$],[$Year $3($$$)]]],[$Warehouse expansion $(1),6,000,2,500,3,500,3,500],[$Basic research $(2),8,000,5,000,1,000,4,000],[$New equipment $(3),3,000,1,000,500,900],[$Advertising campaign $(4),4,000,2,000,1,500,1,800]]$

Let $x_i=1$ if choose project $)=(1,2,3,4$ if not.

Write down your objective function $($include $mi\frac{n}{m}ax$ with the equation$)$ and constraints below, include descriptions$/$explanations$/$calculations on the right. Delete$/$add rows as needed.

$\backslash$table$[[],[($objective function above, constraints below$)],[],[],[],[],[],[],[]]$