Question

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 $0.41, on one serving of Dial 911, $0.54. Each serving of Wimpy requires 0.21 pound of beef, 0.21 cup of onions, and 5 ounces of Kilgore’s special sauce. Each serving of Dial 911 requires 0.21 pound of beef, 0.36 cup of onions, 2 ounces of Kilgore’s special sauce, and 5 ounces of hot sauce. Today, Kilgore has 16 pounds of beef, 11 cups of onions, 85 ounces of Kilgore’s special sauce, and 56 ounces of hot sauce on hand.

A)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=$?

Answer 1

Answer)

Total available beef = 16 pounds

available onions = 11 cups

special sauce 85 + 1 = 86 ounce (as it is mentioned i9n the question that increase the amount of special sauce available by 1 ounce)

hot sauce = 56 ounce

let us define two variables for wimpy and dial 911

x = wimpy

y = dial 911

according to the question,

wimpy requires 0.21 pound of beef and dial 911 requires 0.21 pound of beef and total available beef is 16 pounds

so, 0.21x + 0.21y <= 16 ...................... equation 1

similarly for onions

0.21x + 0.36y <= 11 ............................. equation 2

similarly for the special sauce

5x + 2y <= 86 ...................................... equation 3

for hot sauce

0*x + 5y <= 56 ....................................... equation 4

from equation 4, y = 56/5

y = 11.2

71 7614 Hin 3 (IL,

now by the above graph, we can see that common points are

(0,11.2), (12.72,11.2), (17.2,0), (0,0)

all the points are clear except (12.72,11.2)

to calculate that, consider the equation of line 5x+2y = 86

from this after substituting, y = 11.2

x = 12.72

now the equation of the cost is

0.41x + 0.54y

as profit on wimpy is 0.41 and profit on dial 911 is 0.54

now substituting all the common points in this equation

we get

for(0,0)

0.41*0 + 0.54*0 = $0

for (12.72,11.2)

0.41*12.72 + 0.54*11.2 = $11.26

for (17.2,0)

0.41*17.2 + 0 = $7.052

for(0, 11.2)

0 + 11.2*0.54 = 6.058

clearly profit is maximum for (12.72, 11.2)

so w = 12.72, D = 11.2 and profit = $11.26