$($Capital rationing$)$ The Cowboy Hat Company of Stillwater, Oklahoma, is considering seven capital investment proposals for which the total funds available are limited to a maximum of $$11$ million. The projects are independent and have the costs and profitability indexes associated with them shown in the popup window:

a$.$ Under strict capital rationing, which projects should be selected?

b$.$ What problems are there with capital rationing?

a$.$ Under strict capital rationing, which projects should be selected? $($Select the best choice below.$)$

A$.$ Projects $D$ and $E$

B$.$ Projects D$,$ F and G

C$.$ Projects C$,$ D and E

D$.$ Projects $C$ and $F$

E$.$ Projects C and D

$($Click on the following icon $$ in order to copy its contents into a spreadsheet.$)$

$\backslash$table$[[$PROJECT$,$COST,PROFITABILITY INDEX$],[$A$,$$$2,000,000,1\mathrm{.}13],[$B$,3,000,000,1\mathrm{.}07],[$C$,6,000,000,1\mathrm{.}39],[$D$,5,000,000,1\mathrm{.}34],[$E$,2,000,000,1\mathrm{.}16],[$F$,6,000,000,1\mathrm{.}25],[$G$,3,000,000,1\mathrm{.}19]]$