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

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

$s.t.4,400ozof$ whole tomatoes

$5W+7M,2,240ozof$ tomato sauce

$3W+1M,1,600ozof$ tomato paste

$2W+2M,$

$W,M0,$

The computer solution is shown below.

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

$($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{.}188.$

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

One additional ounce of whole tomatoes will improve profits by $$240\mathrm{.}00.$

Additional ounces of whole tomatoes will not improve profits.

cenetraint $2$

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

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

One additional ounce of tomato sauce will improve profits by $$240\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{.}188.$

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

One additional ounce of tomato paste will improve profits by $$240\mathrm{.}00.$

Additional ounces of tomato paste will not improve profits.

constraint $1$

to

constraint $2$

to

constraint $3$