ounces.

$W=$ jars $of$ Western Foods Salsa

$M=$ jars $of$ Mexico City Salsa

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

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

$s.t.$

$5W+7M4,400ozof$ whole tomatoes

$3W+1M2,400ozof$ tomato sauce

$2W+2M1,600ozof$ tomato paste

$W,M0$

The computer solution is shown below.

Optinal Objective Value $=850\mathrm{.}00000$

Variable Value Reduced Cost

w $,600\mathrm{.}00000,0\mathrm{.}00000$

$M,200\mathrm{.}00000,0\mathrm{.}00000$

Constraint slack$/$Surplus Dual Value

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

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

$2,400\mathrm{.}00000,0\mathrm{.}00000$

$30\mathrm{.}00000,0\mathrm{.}18750$

Variable objective Allowable allowale

Coefficient

alowabl

ncrease

$0\mathrm{.}25000$

Allowable

$0\mathrm{.}10714$

Constraint

RHS Allowable

Increase

Allowable

Decrease

$400\mathrm{.}00000$

$400\mathrm{.}00000$

$342\mathrm{.}85714$

$($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

Mexico City Salsa

$($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 $$400\mathrm{.}00.$

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

Additional ounces of whole tomatoes will not improve profits.

constraint $2$

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.$

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

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 $$400\mathrm{.}00.$

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

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

constraint $2$

to NO LIMIT

constraint $3$

to