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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 $$0\mathrm{.}49,$ on one serving of Dial $911,$ $$0\mathrm{.}55.$ Each serving of Wimpy requires $0\mathrm{.}19$ pound of beef, $0\mathrm{.}19$ cup of onions, and $5$ ounces of Kilgore$$s special sauce. Each serving of Dial $911$ requires $0\mathrm{.}19$ pound of beef, $0\mathrm{.}36$ cup of onions, $2$ ounces of Kilgore$$s special sauce, and $5$ ounces of hot sauce. Today, Kilgore has $14$ pounds of beef, $14$ cups of onions, $84$ ounces of Kilgore$$s special sauce, and $54$ 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

Max fill in the blank $1$

W $+$ fill in the blank $2$

D

s$.$t$.$

fill in the blank $3$

W $+$ fill in the blank $4$

D

fill in the blank $6$

$($Beef$)$

fill in the blank $7$

W $+$ fill in the blank $8$

D

fill in the blank $10$

$($Onions$)$

fill in the blank $11$

W $+$ fill in the blank $12$

D

fill in the blank $14$

$($Special Sauce$)$

fill in the blank $15$

W $+$ fill in the blank $16$

D

fill in the blank $18$

$($Hot Sauce$)$

W$,$ D $>=0$

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

W $=$ fill in the blank $19$

$,$ D $=$ fill in the blank $20$

$,$ Profit $=$ $ fill in the blank $21$

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

$ fill in the blank $22$

Interpret the shadow price.

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

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

W $=$ fill in the blank $24$

$,$ D $=$ fill in the blank $25$

$,$ Profit $=$ $ fill in the blank $26$

Does the solution confirm the answer to part $($c$)?$