It is not necessary that the L.P.P has always an optimum solution.some time it may be no solution.
4. Consider our standard LP: maxc.x subject to Ax <b and x > 0. Assume every...
2. Consider the LP maximize subject to 7.0 2.0 0 3.0 +8.02 +22 < 5 +2.r2 < 4 +3.62 27 21,12 > 0 Explain, without solving the LP, that any optimal solution (yi, y, y37 of the dual problem must satisfy y = 0. Deduce what happens to the optimal value of the primal problem if we replace 27 in the third constraint by 29.
Consider the following LP problem. minimize 3:01 +4.c3 subject to 2:01 + x3 - I3 < -2 21 +3.02 – 5x3 = 7 21 <0,22 > 0, 03 free Which of the LP problem below is its dual problem? maximize -2p1 + 7p2 subject to 2p. + P23 1 + 3p2 50 -P1 - 5p2 = 4 Vi < 0,2 > 0 maximize --2p1 + 702 subject to 2p. + P23 1 + 3p2 50 -P1 - 5p2 = 4...
Question 2: Identify which of Cases (1)--(4) apply to the following LP problem. max z = 2x1 – X2 s. t. X1 – X2 < 1 2x1 + x2 > 6 X1, X2 > 0 (1) unbounded LP (2) infeasible LP (3) unique optimal solution (4) multiple optimal solutions
Problem A: Consider the following LP problem to answer Questions 4 and 5. Maximise z = 5x1 + 4x2 Subject to 6X1 + 4x2 < 24 X1 + 2x2 5 6 -X1 + x2 <1 X2 < 2 X1, X2 > 0 Question 4 Refer to Problem A: Which of the following statements is correct? (1) The optimal value of x1 is in the interval [10, 15). (2) The optimal valu X2 is in the rval [0, 5). (3) The...
[1.38] Consider the problem: Minimize cx subject to Axb, x>0. Suppose that one component of the vector b, say bị, is increased by one unit to b; + 1. a. What happens to the feasible region? b. What happens to the optimal objective value?
3. Consider the following LP. Maximize u = 4x1 + 2x2 subject to X1 + 2x2 < 12, 2x1 + x2 = 12, X1, X2 > 0. (a) Use simplex tableaux to find all maximal solutions. (b) Draw the feasible region and describe the set of all maximal solutions geometrically.
2. For the difference cquation, X2+] = ax, + b = f(x,), where 0 <a < 1 and b> 0, use the solution given in (1.12) to find the following limit: lim ->XX7. Show that this limit is also a fixed point of the difference cquation, that is, it is a solution x of t = f(x) (see Figure 1.2).
[5.53] Consider the problem: Minimize cx subject to Ax = b, x 2 0. Let x* be the unique optimal extreme point. Show that the second best extreme point must be adjacent to x*. What happens if the uniqueness assumption is relaxed?
1. Floating point arithmetic. The standard formula for solving ax² +bx+c=0 is -b±/b² – 4ac 2a = Fx However, if b² > closest to zero. Why is this, and how can you avoid this problem? Jac| this can give inaccurate results, at least for the root
SOLVE STEP BY STEP! 4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...