Obtain the dual of the following primal LP problem:
Maximize z = x1 - 2x2 + 3x3
Subject to -2x1 + x2 + 3x3 = 2
2x + 3x2 + 4x3 =1
X1,X2X2 ≥ 0
To obtain the dual of the given primal Linear Programming (LP) problem, we follow these steps: ### Step 1: Identify Primal Problem #### Primal LP: \[ \text{Maximize } z = x_1 - 2x_2 + 3x_3 \] Subject to: \[ -2x_1 + x_2 + 3x_3 = 2 \] \[ 2x_1 + 3x_2 + 4x_3 = 1 \] \[ x_1, x_2, x_3 \geq 0 \] ### Step _______ ________ _____ ______ __________ ________ ________ __________ ____.
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State which of the following statements are true and which are false. Give reasons for your answer with a short proof or a counter example.
a) The intersection of finite number of convex sets is not convex.
b) If value of the 2× 2 matrix game is 4, then p ≥ 4 .
c) If 10 is added to each of the entries of the cost matrix of a 3× 3 assignment problem, then the total cost of an optimal assignment for the changed cost matrix will increase by 10.
d) For maximization LP model, the simplex method is terminated when all values cj − zj ≥ .0
e) The dummy source or destination in a transportation problem is added to prevent solution from becoming degenerate.
Two breakfast food manufacturers ABC and XYZ are competing for an increased market share. The pay-off matrix, shown in the following table, describes the increase in market share for ABC and decrease in market share of XYZ. Determine optimal strategies for both the manufacturers and the value of the game.
Find the initial basic feasible solution of the following transportation problem using North-West Corner method.
| 90 | 90 | 100 | 110 | 200 |
| 50 | 70 | 130 | 85 | 50 |
| 75 | 100 | 100 | 30 |
k के किस मान के लिए निम्नलिखित सदिश, रैखिकतः स्वतंत्र हैं?
For what value of k are the following vectors linearly independent?
निम्नलिखित परिवहन समस्या की (LPP) सूचित कीजिए :
| Destination | Supply | |||||||||
| D1 | D2 | D3 | ||||||||
| O1 | 10 | 18 | 12 | 200 | ||||||
| Source | O2 | 15 | 17 | 9 | 300 | |||||
| O3 | 13 | 15 | 7 | 500 | ||||||
| Requirement | 400 | 200 | 400 | |||||||
Find all values of k for which the vectors:
are linearly independent.