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Problem 4-05 (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 $0.35, on one serving of Dial 911, $0.59. Each serving of Wimpy requires 0.45 pound of beef, 0.45 cup of onions, and 5 ounces of Kilgore’s special sauce. Each serving of Dial 911 requires 0.45 pound of beef, 0.72 cup of onions, 1 ounces of Kilgore’s special sauce, and 4 ounces of hot sauce. Today, Kilgore has 33 pounds of beef, 47 cups of onions, 81 ounces of Kilgore’s special sauce, and 48 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 = # of servings of Wimpy to make D = # of servings of Dial 911 to make Max 0.35 | W 0.59 D 33 (Beef) 47 | |(Onions) 81-、〈, |(Special Sauce) 48 V(Hot Sauce) 0.45 W 0.45 D 0.45 W 0.72V D 1 4 b. Find an optimal solution. Round the answer for profit to the nearest cent and, if required, round the answers for W and D to one decimal
Expert Answer
| Let wimpy is represented by W and Dial911 I repreented by D | ||||||||||||||||
| LP will be Max = W*0.35+D*0.59 subject to 0.45*W+0.45*D<=33 , 0.45*W+0.59*D<=47 , 5*W+1*D<=81 , 4*D<=48 & W and D >=0 | ||||||||||||||||
| Now let us use a spreadsheet and solve it through solver. | ||||||||||||||||
| Production Plan | Wimpy | W | 13 | |||||||||||||
| Dial 911 | D | 12 | ||||||||||||||
| Wimpy | Dial 911 | |||||||||||||||
| Available | Balance | Consumption per serving | Production Servings | Total consumption | Profit per Serving | Total Profit | Consumption per serving | Production Servings | Total consumption | Profit per Serving | Total Profit | Total Profit on Wimpy and Dial 911 | ||||
| 1 | 2=1-3*4-8*9 | 3 | 4 | 5=3*4 | 6 | 7=4*6 | 8 | 9 | 10=8*9 | 11 | 12=9*11 | 13=7+11 | ||||
| Beef | B | pounds | 33 | 21.75 | 0.45 | 13 | 5.85 | 0.35 | 4.55 | 0.45 | 12 | 5.4 | 0.59 | 7.08 | 11.63 | |
| Onions | O | cups | 47 | 32.51 | 0.45 | 13 | 5.85 | 0.72 | 12 | 8.64 | ||||||
| Special Sauce | S | ounces | 81 | 4 | 5 | 13 | 65 | 1 | 12 | 12 | ||||||
| Hot Sauce | H | ounces | 48 | 0 | 0 | 13 | 0 | 4 | 12 | 48 | ||||||
| So as per the solver W should be 13 and D should be 12 servings | ||||||||||||||||
| & Profit is $ 11.63 | ||||||||||||||||
| Now if we increase the special sauce availability by 1 ounce. | ||||||||||||||||
| Production Plan | Wimpy | W | 14 | |||||||||||||
| Dial 911 | D | 12 | ||||||||||||||
| Wimpy | Dial 911 | |||||||||||||||
| Available | Balance | Consumption per serving | Production Servings | Total consumption | Profit per Serving | Total Profit | Consumption per serving | Production Servings | Total consumption | Profit per Serving | Total Profit | Total Profit on Wimpy and Dial 911 | ||||
| 1 | 2=1-3*4-8*9 | 3 | 4 | 5=3*4 | 6 | 7=4*6 | 8 | 9 | 10=8*9 | 11 | 12=9*11 | 13=7+11 | ||||
| Beef | B | pounds | 33 | 21.3 | 0.45 | 14 | 6.3 | 0.35 | 4.9 | 0.45 | 12 | 5.4 | 0.59 | 7.08 | 11.98 | |
| Onions | O | cups | 47 | 32.06 | 0.45 | 14 | 6.3 | 0.72 | 12 | 8.64 | ||||||
| Special Sauce | S | ounces | 82 | 0 | 5 | 14 | 70 | 1 | 12 | 12 | ||||||
| Hot Sauce | H | ounces | 48 | 0 | 0 | 14 | 0 | 4 | 12 | 48 | ||||||
| Here W will increase to 14 and D will be 12 servings | ||||||||||||||||
| & Profit is $ 11.98 | ||||||||||||||||
| Please explain what is meant by Dual Value of Special Sauce . If it is combined consumption then it is 77 ounces for option 1 availability of special sauce is 81 ounces. | ||||||||||||||||
