$\backslash$table$[[$Variable$,$Value,Reduced Cost,$],[W,600\mathrm{.}00000,0\mathrm{.}00000,],[M,200\mathrm{.}00000,0\mathrm{.}00000,],[$Constraint$,$Slack$/$Surplus$,$Dual Value$],[1,0\mathrm{.}0000,0\mathrm{.}12500],[2,400\mathrm{.}0000,0\mathrm{.}00000],[3,0\mathrm{.}0000,0\mathrm{.}18750],[$Variable$,\backslash$table$[[$Objective$],[$Coefficient$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[$W$,1\mathrm{.}00000,0\mathrm{.}25000,0\mathrm{.}10714],[M,1\mathrm{.}25000,0\mathrm{.}15000,0\mathrm{.}25000],[$Constraint$,\backslash$table$[[$RHS$],[$Value$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[1,4400\mathrm{.}00000,1200\mathrm{.}00000,400\mathrm{.}00000],[2,2400\mathrm{.}00000,$Infinite,$400\mathrm{.}00000],[3,1600\mathrm{.}00000,100\mathrm{.}00000,342\mathrm{.}85714]]$

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

$\backslash$table$[[$W$,$jars$],[$M$,$jars$],[$profit $$,]]$

$($b$)$ Specify the objective function ranges. $($Round your answers to five decimal places.$)$

Western Foods Salsa to

Mexico City Salsa to

$($c$)$ What are the dual values for each constraint? Interpret each.

constraint $1$

One additional ounce of whole tomatoes will improve profits by $$0\mathrm{.}125.$

One additional ounce of whole tomatoes will improve profits by $$0\mathrm{.}188.$

One additional ounce of whole tomatoes will improve profits by $$400,00.$

Additional ounces of whole tomatoes will not improve profits.