A linear programming computer package is needed.

Kilgore's Deli is a small delicatessen located near a major university. Kilgore 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 $\backslash (\backslash$$ $0\mathrm{.}46\backslash ),$ on one serving of Dial $\backslash (911,\backslash$$ $0\mathrm{.}59\backslash ).$ Each serving of Wimpy requires $0\mathrm{.}25$ pound of beef, $0\mathrm{.}25$ cup of onions, and $5$ ounces of Kilgore's special sauce. Each serving of Dial $911$ requires $0\mathrm{.}25$ pound of beef, $0\mathrm{.}4$ cup of onions, $2$ ounces of Kilgore's special sauce, and $5$ ounces of hot sauce. Today, Kilgore has $21$ pounds of beef, $16$ cups of onions, $89$ ounces of Kilgore's special sauce, and $61$ ounces of hot sauce on hand.

$($a$)$ Develop an linear programming model that will tell Kilgore how many servings of Wimpy and Dial $911$ to make in order to maximize his profit today. $($Let $\backslash ($ W$=\backslash )$ the number of servings of Wimpy to make and let $\backslash ($ D$=\backslash )$ the number of servings of Dial $911$ to make.$)$

Max

s$.$t$.$

Beef

Onions

Special Sauce

Hot Sauce

$\backslash [$

W$,$ D $\backslash$geq $0$

$\backslash ]$

$($b$)$ Find an optimal solution. $($Round your answers to two decimal places.$)$

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

$($W$,$ D$)=(\backslash \backslash$

$\backslash$text $\{$ Profit $\}=\backslash$$

$\backslash$end$\{$array$\}$

$\backslash ]$

$($c$)$ What is the shadow price for special sauce? $($Round your answer to two decimal places.$)$

$\backslash$$

Interpret the shadow price.

For every $1$ ounce increase in

$,$ the profit will

by $\backslash$$

$($d$)$ Increase the amount of special sauce available by $1$ ounce and re$-$solve. $($Round your answers to two decimal places.$)$

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

$($W$,$ D$)=(\backslash \backslash$

$\backslash$text $\{$ Profit $\}=\backslash$$

$\backslash$end$\{$array$\}$

$\backslash ]$

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

Yes

No