Without sketching the region, check whether is in the convex hull of the points
and
. If it is in the region, write P as convex combination of A,B and C.
To determine whether \( P(0,0) \) is in the convex hull of \( A(-1,-1) \), \( B(1,0) \), and \( C(0,1) \), we need to check if we can express \( P \) as a convex combination of \( A, B, \) and \( C \). That is, we need to find real numbers \( \lambda_1, \lambda_2, \lambda_3 \) ________ _____ _____ __________ __________ ____.
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Solve by simplex method the following linear programming problem:
Solve, graphically, the game whose pay-off matrix is:
a) A marketing manager has 5 salespersons and 5 sales districts. Considering the capabilities of the salespersons and the nature of the districts, the marketing manager estimates the sales per month (in thousand 
) for each salesperson in each distinct as follows
Salespersons
| Districts | |||||
| 1 | 2 | 3 | 4 | 5 | |
| A | 32 | 38 | 40 | 28 | 40 |
| B | 40 | 44 | 28 | 21 | 36 |
| C | 41 | 27 | 33 | 30 | 37 |
| D | 22 | 38 | 41 | 36 | 36 |
| E | 29 | 33 | 40 | 35 | 39 |
Show that the set of vectors
from a basis for
Which of the following statements are true and which are false? Give reasons for your answer.
a) In an LP model, the feasible solution space can be effected when redundant constraints are deleted.
b) If the primal LPP has an optimal solution, then the set of feasible solution to its dual is bounded.
c) In a simplex iteration, an artificial variable can be dropped all together from the simplex table once the variable becomes non basic.
d) The addition of a constant to all the elements of a payoff matrix in a two – person zero sum game can affect only the value of the game, not the optimal mix of the strategies.
e) There may be a balanced transportation problem without any feasible solution.
Find the maximum and minimax values of the following matrix game.
Does the matrix have a saddle point. Justify your answer.
Using the principle of dominance, solve the game whose pay-off matrix is given below:
