Consider the following linear program:
Max | 2A | + | 10B | ||
s.t. | |||||
3A | ≤ | 15 | |||
B | ≤ | 6 | |||
4A | + | 4B | = | 28 | |
A, B ≥ 0 |
a. draw graph that shows the feasible region for the problem
b. What are the extreme points of the feasible region
c. Draw graph that shows the optimal solution for the problem
Consider the following linear program: Max 2A + 10B s.t. 3A ≤ 15 B ≤ 6...
Consider the following linear program: Max. 2A + 10B s.t. 3A ≤ 15 B ≤ 6 4A + 4B = 28 A, B ≥ 0 a.) Plot a graph that shows the feasible region for the problem b.) What are the extreme points of the feasible region
For the linear program Max 3A+2B s.t. A+B>=4 3A+4B<=24 A>=2 A-B<=0 A, B>=0 a. Write the problem in standard form. b. Solve the problem. c. What are the values of the slack and surplus variables at the optimal solution?
For the linear program Max 3 A + 3 B s.t. A + 2B ≤ 8 5A + 3B ≤ 15 A, B ≥ 0 Draw graph that identifies the optimal solution. What is the value of the objective function at the optimal solution?
Consider the following linear program: Min 3A + 48 +28 26 AB 20 2. Select the correct graph that shows the feasible region and the optimal solution for the problem. 0 (1) 10 8 Optimal Solution: A-2, B-2 - Optional Solution And, BM A (iv) Optimal Solution: A-0, B- Optimal Solution: A=2, B-2 b. What is the value of the objective function? If required, round your answer to one decimal place. Objective function value:
business Problem 2-19 Consider the finear program Max 34 + 40 s.t. 1A+ 28s 8 1A28s 12 2A+ 18s 16 A, 82 0 or leave the box blank the model, enter 0 for a. Write the problem in standard form, For those boxes n which you must enter sueractive or neostive nmbers use a meus sign, (Example:-300) f you dot need the vanable A. S e S St Max s.t. s A+ S A+ A, B, St, Sa, S b....
2. Consider the following linear model where C1 has not yet been defined. Max s.t. z = C1x1 + x2 X1 + x2 = 6 X1 + 2.5x2 < 10 X1 > 0, x2 > 0 Use the graphical approach that we covered to find the optimal solution, x*=(x1, xỉ) for all values of -00 < ci so. Hint: First draw the feasible region and notice that there are only a few corner points that can be the optimal solution....
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2 〈 24 1xl t 2x2< 16 And xl, x2> 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of xl, x2, and Z. b) Assume that the objective function coefficient for xl changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective...
Problem 3-02 (Algorithmic) Consider the following linear program: Max 3A 2B 1A 1B s 12 1A 2B s 20 A, B 2 0 The value of the optimal solution is 31. Spose that the right-hand side of the constraint 1 is increased from 12 to 13. a. Use the graphical solution procedure to find the new optimal solution. 26 Optimal Solahion A6584 2B-325 28-39 20 12-14 16 11 1012 14 1618 nv) B Optimal Solution 23-26 26 30 2 34...
Let (IP) be the following integer program: max (0, -1). s.t. 1-1 -107 -10 10 -11</-0.5 1-10 / 0 z integer Let (LP) be the LP relaxation of (IP). We draw the feasible region of (LP) here. 2. . . . . . . to (LP), and prove that it is optimal by providing a (a) Determine an optimal solution certificate of optimality.
1. (20 pts.) Consider the following linear program: max 4x4 +xz+5x3 +3x4 s.t. *1 -X2 -X3 +3X, 51 5x +xz+3X3 +8X555 -X2 +2x2+3x3 -5x53 It is claimed that the solution x* = (0,14,0,5) is an optimal solution to the problem. Give a proof of the claim. Do not use the simplex method to solve this problem.