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 $$0\mathrm{.}44,$ on one serving of Dial $911,$$$0\mathrm{.}57.$ 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 $18$ pounds of beef, $13$ cups of onions, $86$ ounces of Kilgore's special sauce, and $58$ ounces of hot sauce on hand.

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

Max

s$.$t$.$

Beef

Onions

Special Sauce

Hot Sauce

$W,D0$

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

$(W,D)=()$

Profit $=$$

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

$

Interpret the dual value.

For every $1$ ounce increase in $,$ the profit will by $

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

$(W,D)=()$