Consider the following all-integer linear program: max 5x1 + 8x2 s.t. 9x1 + 4x2 ≤ 36 1x1 + 2x2 ≤ 10 x1, x2 ≥ 0 and integer.
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Consider the following all-integer linear program:
max 5x1 + 8x2
s.t. 9x1 + 4x2 ≤ 36
1x1 + 2x2 ≤ 10
x1, x2 ≥ 0 and integer.
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- minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2Fopic 4- Linear Programming: Appli eBook 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 $0.46, on one serving of Dial 911, $0.59. Each serving of Wimpy requires 0.26 pound of beef, 0.26 cup of onions, and 6 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.26 pound of beef, 0.41 cup of onions, 3 ounces of Kilgore's special sauce, and 6 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 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.…Solve the following Linear Programming model using the graphical method (USING EXCEL){Write the steps of construction} Q1)MaximizeH = x + 3y Objective functionsubject tox + y ≤ 502x + y ≤ 60 x ≥ 0, y ≥ 0
- Scenario You are going to plant a rectangular flower bed consisting of tulips in the middle surrounded by daisies on the outside. You have the same amount of each flower and will need an equal area for each. You want the border of daisies to be uniform around the tulips in the middle, as shown in the diagram below:Simplex Method Example Maximize :P = 4x, + 3x, +2x3 |3x, + 2х, + 5х, < 23 2x, + x, + x, <8 X, + x, + 2x, s7 3x, +2x, +5x, +s, = 23 2x, + x, + X3 +S2 = 8 x, + X, +2x, +s, =7 (- 4x, – 3x, -2x, +P = 0 System: ST : X1, X2, X3 2 0 X2 X3 s, S2 s, P 1 0 0 0| 23 0 1 0 0 23 +3 = 7.6 8+2=(4) 3 2 5 s2 [2] 1 1 8 1 S3 1 2 0 0 1 0 7 7÷1= 7 Р(-4) -3 -2 0 о 01 - 3R, + R, → R, 1 Row Operations:R, → R, - R, + R, → R, and 4R, + R4 → R4 X2 X3 S2 S3 P [o 1/2 7/2 1 -3/2 0 0|11]11+(1/2) = 22 1/2 1/2 0 o 0| 4 4+ (1/2) = 8 X|1 s3 0 {1/2} 3/2 0 -1/2 1 0 3 3-(1/2) = 6 P0 (-1) o 0 X1 enters to become a basic variable, s2 exits to become a nonbasic variable (pivot column identifies the entering variable and pivot row identifies the exiting variable) 1/2 2 0 1 16 R, + R¸ → R, Row Operations: 2R, → R, and R3 + R2 → R, R, + R, → R4 S3 P 1 -1 -1 0 -1 0 X, X2 X3 S, S2 S0 0 Final Tableau x, 1 0 -1 0 2 8 1 1 2 0 6 2 1 22 X2 0 1 3 0 -1 PO 0 3 0 1 X2 enters to become a basic variable, s3 exits to become a nonbasic variable…Determine the pivot element in the simplex tableau. (If there is more than one correct pivot element, choose the element with the smaller row number.) X1 X2 X3 S1 S2 3 4 2 1 15 1 20 -8 -3 10 1 row column N O O
- Consider the following Pareto maximization problem with decision variables x and y: vmax (x2 + x, - 2y) s.t. 0< x< 10 0< y< 5. What is the unique efficient point for this problem? (0,0) (10,5) (10,0) (110,0)Consider the following puzzle. You are to pick out 4three-letter “words” from the following list:DBA DEG ADI FFD GHI BCD FDF BAIFor each word, you earn a score equal to the position thatthe word’s third letter appears in the alphabet. For example,DBA earns a score of 1, DEG earns a score of 7, and so on.Your goal is to choose the four words that maximize yourtotal score, subject to the following constraint: The sum ofthe positions in the alphabet for the first letter of each wordchosen must be at least as large as the sum of the positionsin the alphabet for the second letter of each word chosen.Formulate an IP to solve this problem.Maximize p = 7x + 6y + 3z subject to x + y + z ≤ 150 x + y + z ≥ 100 x ≥ 0, y ≥ 0, z ≥ 0. p= (x, y, z)=