$10\%$ tomato sauce, and $20\%$ tomato paste. Each jar of salsa produced weighs $10$ ounces.

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$)$:

The computer solution is shown below.

Optimal Objective Value $=870\mathrm{.}00000$

M $280\mathrm{.}000000\mathrm{.}00000$

Constraint Slack$/$Surplus Dual Value

$0\mathrm{.}000000\mathrm{.}12500$

$400\mathrm{.}000000\mathrm{.}00000$

Variable Objective Allowable Allowable

W $1\mathrm{.}000000\mathrm{.}250000\mathrm{.}10714$

M $1\mathrm{.}250000\mathrm{.}150000\mathrm{.}25000$

Constraint rHS Allowable Allowable

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

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\mathrm{.}00.$

Additional ounces of whole tomatoes will not improve profits.

constraint $2$

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

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

One additional ounce of tomato sauce will improve profits by $$400\mathrm{.}00.$

Additional ounces of tomato sauce will not improve profits.

constraint $3$

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

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

One additional ounce of tomato paste will improve profits by $$400\mathrm{.}00.$

Additional ounces of tomato paste will not improve profits.

$($d$)$ Identify each of the right$-$hand$-$side ranges. $($Round your answers to two decimal places. If there is no upper or lower limit$,$ enter NO LIMIT.$)$

constraint $1$

to $4$

constraint $2$

to

constraint $3$

to