which has a thicker and chunkier consistency, consists of $70\%$ whole tomatoes, $10\%$ tomato sauce, and $20\%$ tomato paste. Each jar of salsa produced weighs $10$ ounces. Tom's contract with Western Foods results in sales revenue of $$1\mathrm{.}64$ for each jar of Western Foods Salsa and $$1\mathrm{.}93$ for each jar of Mexico City Salsa. Letting

$W=$ jars $of$ Western Foods Salsa

$M=$ jars $of$ Mexico City Salsa

leads to the formulation $($units for constraints are ounces$)$:

Max $1W+1\mathrm{.}25M,$

$s.t.$

$5W+7M,4,560ozof$ whole tomatoes

$3W+1M,2,400ozof$ tomato sauce

$2W+2M,1,600ozof$ tomato paste

$W,M0,$

The computer solution is shown below.

$])$:$\}$

$W520\mathrm{.}00000,0\mathrm{.}00000$

$M280\mathrm{.}00000,0\mathrm{.}00000$

$,$

Constraint $$1ac\frac{k}{s}$urplus Dual Value

$1,0\mathrm{.}00000,0\mathrm{.}12500$

$2,560\mathrm{.}00000,0\mathrm{.}00000$

$[3,0\mathrm{.}00000,0\mathrm{.}18750$

$\backslash$table$[[$Variable$,\backslash$table$[[$Objective$],[$Coefficient$]],\backslash$table$[[$Allowable$],[$Increase$],[0\mathrm{.}25000]],\backslash$table$[[$Allowable$],[$Decrease$],[0\mathrm{.}10714]]],[$W$,1\mathrm{.}00000,0\mathrm{.}15000,0\mathrm{.}25000],[$M$,1\mathrm{.}25000,0,],[$Constraint$,\backslash$table$[[$RHS$],[$Value$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[1,4560\mathrm{.}00000,1040\mathrm{.}00000,560\mathrm{.}00000],[2,2400\mathrm{.}00000,$Infinite,$560\mathrm{.}00000],[3,1600\mathrm{.}00000,140\mathrm{.}00000,297\mathrm{.}14286]]$

$($a$)$ What is the optimal solution, and what are the optimal production quantities?

w jars

M jars

profit $