Problem $9-05($Algorithmic$)$

Kilgore$$s Deli is a small delicatessen located near a major university. Kilgore$$s does a large walk$-$in carry$-$out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial $911.$ At the beginning of the day, Kilgore needs to decide how much of each specia Problem $9-05($Algorithmic$)$

Kilgore's Deli is a small delicatessen located near a major university. Kilgore's does a large walk$-$in carry$-$out lunch business. The

deli offers two luncheon chili specials, Wimpy and Dial $911.$ At the beginning of the day, Kilgore needs to decide how much of

each special to make $($he always sells out of whatever he makes$).$ The profit on one serving of Wimpy is $$0\mathrm{.}43,$ on one serving of

Dial $911,$$$0\mathrm{.}56.$ Each serving of Wimpy requires $0\mathrm{.}23$ pound of beef, $0\mathrm{.}23$ cup of onions, and $5$ ounces of Kilgore's special sauce.

Each serving of Dial $911$ requires $0\mathrm{.}23$ pound of beef, $0\mathrm{.}38$ cup of onions, $2$ ounces of Kilgore's special sauce, and $5$ ounces of hot

sauce. Today, Kilgore has $18$ pounds of beef, $13$ cups of onions, $87$ ounces of Kilgore's special sauce, and $58$ ounces of hot sauce

on hand.

a$.$ Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial $911$ to make in order to

maximize his profit today. If required, round your answers to two decimal places. For subtractive or negative numbers use a

minus sign even if there is a $+$ sign before the blank. $($Example: $-300)$

Let $W=$ number of servings of Wimpy to make

$D=$ number of servings of Dial $911$ to make

b$.$ Find an optimal solution. If required, round your answers to two decimal places.

$W=$

$,D=$

Profit $=$$

c$.$ What is the shadow price for special sauce? If required, round your answers to two decimal places. b$.$ Find an optimal solution. If required, round your answers to two decimal places.

$W=$

$,$ Profit $=$$

c$.$ What is the shadow price for special sauce? If required, round your answers to two decimal places.

$

Interpret the shadow price.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

d$.$ Increase the amount of special sauce available by $1$ ounce and re$-$solve. If required, round your answers to two decimal

places.

$W=$

$,D=$

$,$ Profit $=$$

Does the solution confirm the answer to part $($c$)?$l to make $($he always sells out of whatever he makes$).$ The profit on one serving of Wimpy is $$0\mathrm{.}43,$ on one serving of Dial $911,$ $$0\mathrm{.}56.$ Each serving of Wimpy requires $0\mathrm{.}23$ pound of beef, $0\mathrm{.}23$ cup of onions, and $5$ ounces of Kilgore$$s special sauce. Each serving of Dial $911$ requires $0\mathrm{.}23$ pound of beef, $0\mathrm{.}38$ cup of onions, $2$ ounces of Kilgore$$s special sauce, and $5$ ounces of hot sauce. Today, Kilgore has $18$ pounds of beef, $13$ cups of onions, $87$ ounces of Kilgore$$s special sauce, and $58$ ounces of hot sauce on hand.

Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial $911$ to make in order to maximize his profit today. If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a $+$ sign before the blank. $($Example: $-300)$

Let W $=$ number of servings of Wimpy to make

D $=$ number of servings of Dial $911$ to make