Here we have olve thi problem using graphical method
Question 1. (30 points) You are provided with the following integer program: max := 3x +...
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...
Consider the following constraints and the corresponding graph below Constraint 1: 2x-y21 Constraint 2:x+2y S8 Constraint 3: x-3y 2-2 2x-y-1 4 x +2y 8 4 7 a. (3 points) Shade the feasible region in the graph provided above. b. (3 points) The objective function is Minimize 2x-3y. Mark the optimal solution(s) in the above graph Do not calculate the x and y coordinates at optimal solution(s). Draw the optimal objective function line through the optimal solution(s).
(45 Points) Consider the constrained optimization problem: min f(x1, x2) = 2x} + 9x2 + 9x2 - 6x1x2 – 18x1 X1 X2 Subject to 4x1 – 3x2 s 20 X1 + 2x2 < 10 -X1 < 0, - x2 < 0 a) Is this problem convex? Justify your answer. (5 Points) b) Form the Lagrange function. (5 Points) c) Formulate KKT conditions. (10 Points) d) Recall that one technique for finding roots of KKT condition is to check all permutations...
Consider the following constraints and the c g graph below: Constraint L:4x-y21 Constraint 2: x+ys4 Constraint 3:-x-4y 2-8 x, y20 4x-y=1 x-4y -8 a. (2 points) Shade the feasible region in the graph provided above. b. (1 point) For this part only the objective function is Minimize -2x + y. Which of the following describes the optimal solution? (Put a check next to your answer) Infeasible solution Unique optimal solution the point (4,0) minimizes the LP Alternate optimal solution Unbounded...
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...
Question 4 (3 points) Set up and solve the following simple linear optimization model: MAX: 14.9 x + 23.8 y subject to: 2x + 2y = 20 3x 2 17 5x + 1y s 78 x.y 20 What is the value of the objective function at the optimal solution? Round your answer to one decimal place. Your Answer: Answer Question 5 (8 points) -
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.
Given the system of linear inequalities below. You are completing a maximization problem where you have 2 machines, Machine 1 and Machine 2, which we will identify as M1 and M2. These machines produce 2 products, Product 1 and Product 2, which we identify as P1 and P2. Our objective function is M = 20x + 50y. 3x + y =21 4x +y 27 x 20 (y20 Suppose you are told that the maximum occurs at a vertex (corner point)...
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,...
QUESTION 1 Given the following LP, answer questions 1-10 Minimize -3x15x2 Subject to: 3x2x 24 2x1+4x2 2 28 2s 6 x1, x2 20 How many extreme points exist in the feasible region for this problem? We cannot tell from the information that is provided The feasible e region is unbounded QUESTION 2 Given the following LP, answer questions 1-10 Minimize 2- 31+5x2 Subject to: 3x2x 24 2x1+4x2228 t is the optimal solution? (2, 6) (0, 12) (5,4.5) None of the...