a$.(50$ points$)$ Suppose you have been asked to help determine how many units of your product to be produced at each of five manufacturing facilities that your firm owns. The facilities are identified by the letters A through E$.$ You would like to minimize the collective variable $($i$.$e$.,$ per unit$)$ operating costs across all facilities. Those operating costs as well as the production capacities vary somewhat across all five facilities, as shown in the table below.

$\backslash$table$[[$Facility$,$Eacilitv Canacitv,$\backslash$table$[[$Variable Operating$],[$Costs per Unit$]]],[],[$A$,2200,$$$28\mathrm{.}50$