Let (IP) be the following integer program: max (0, -1). s.t. 1-1 -107 -10 10 -11</-0.5...
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 integer program Max 2x+3y s.t 6x+7y23 x-y<12 xy0 x,y: integer Let V1 denote the optimal objective value of the above optimization problem. Let V2 denote the optimal objective value of the optimization problem obtained by dropping "x,y: integer" constraint. Similarly, let V3 denote the optimal objective value of the optimization problem obtained by dropping "x-y<-12" constraint which one of the following statements is correct? a. V2 V1 and V3<-V1 b. V1 V2 and V1<-V3 c. V2V1 but...
Question 3 : Branch and Bound max 36a1282+8as s.t. 21i + 20r2 6xs 23 a e 10, 1]3 Write the LP Relaxation of this problem. 1. 2. What type of problem is this? (this type of problem has a particular name) Solve this problem by branch-and-bound, using the branching rule for binary variables of branching o 3. the most fractional variable. On the next page, write down the branch-and-bound tree you obtained. a. Each node should include the solution letter,...
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...
Consider the following linear program: Max 2X + 3Y s.t. 5X +5Y ≤ 400 -1X+ 1Y ≥ 10 1X + 3Y ≥ 90 X, Y ≥ 0 a. Use the graphical solution procedure to find the optimal solution. b. Conduct a sensitivity analysis to determine the range of optimality for the objective function coefficients X & Y. c. What are the binding constraints? d. If the right-hand-side of the binding constraints are marginally increased, what will be the Dual Value?
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 all-integer linear program: Max x1+x2 s.t 4x1+6x2 <= 22 x1+5x2<= 15 2x1+x2<=9 x1,x2>=0 integer Solve in Excel Solver and AMPL.
Question 1. (30 points) You are provided with the following integer program: max := 3x + y 8.t. x + 1.6y S8 - 5 + 6x = 15 35.5 x,y20 and integer (a) On the graph provided on the following page, use the graphical solution method to identify the feasible points on your graph. (Use the scale 1 by 1 for each small square so that you can visually detect the feasible integer solutions.) (b) Enumerate the feasible extreme points...
Solve the following linear fractional program: max ? = ?1+2?2+?3+6/ 3?1+?3+5 s.t. ?1 + ?2 + 3?3 ≤ 10 2?1 + 3?2 ≤ 7 ?1,?2,?3 ≥ 0 Let ? = 1/ 3?1+?3+5 and ?1 = ??1,?2 = ??2, ?3 = ??3.
Question 3-Integer Programming (10 points). Let PB be the following binary program. P: min 2x1 x2 3(2x 1)-2x subject to: X3 +x4 21 x, binary x2 binary x binary x, binary 1) What is the number of feasible solutions of Ps? Justify your answer. 2) Using brute force enumeration, give the optimal solution and its objective value Question 3-Integer Programming (10 points). Let PB be the following binary program. P: min 2x1 x2 3(2x 1)-2x subject to: X3 +x4 21...