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.
a) True. Deleting redundant constraints can change the feasible solution space because these constraints are not contributing to the solution and removing them can alter the feasible region.
b) False. The statement is incorrect. If the primal LPP has an optimal solution, then the set of feasible solutions ______ ___ _________ ________ ___ _________ ______ ________ _____.
________ _________ ___ ________ _____ _______ _________ _________ _________ __________.
________ __________ __________ ________ _____ ______ ___ __________ __________.
______ ______ _____ _________ ________ _______ _________ ______ ________ _____ ______ _______.
___ _____ ______ _________ _________ ______ _______ ___ ____ _______.
______ _____ ____ ______ ________ _________ _______ ________ _______ ____ ___ _______.
___ ____ ___ _________ _________ ___ ________.
_____ _______ __________ _____ ______ _________ ___ _____ ___ _______.
_______ ___ __________ _______ _________ ____ __________ ______ ____ _____ ______ __________.
____ ______ _________ ______ _________ _________ ______ _________.
_______ __________ ______ ______ ___ _______ __________.
_____ _________ _____ __________ _________ _____ _____ ______ ___ ____ ________ ____.
____ _______ ______ _____ ______ ___ ________ ______ _________.
_______ __________ _________ ________ _________ __________ ____ __________ __________ _____ ___ ________.
_______ _______ _____ _____ ______ ______.
__________ ___.
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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 |
a) A toy company manufactures two types of doll; a basic version-doll A and a deluxe version-doll B. Each doll of type B takes twice as long as to produce as one of type A, and the company would have time to make a maximum 2000 per day if it produce only the basic version. The supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 600 per day available. The company makes profit of ₹3 and 5 per doll respectively on doll A and B. How many of each should be produced per day in order to maximize profit? Solve this problem by graphical method.a) A toy company manufactures two types of doll; a basic version-doll A and a deluxe version-doll B. Each doll of type B takes twice as long as to produce as one of type A, and the company would have time to make a maximum 2000 per day if it produce only the basic version. The supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 600 per day available. The company makes profit of 3 and 5 per doll respectively on doll A and B. How many of each should be produced per day in order to maximize profit? Solve this problem by graphical method.
b) Find all the basic solutions of the following system:
i) Formulate the dual of the following problem:
ii) Check whether is a feasible solution to the primal and
is a feasible solution to the dual.
iii) Use duality to check whether is an optimal solution to the primal.
Find an initial basic feasible solution for the following transportation problem using matrix-minima method. Also find the transportation cost.
Using the principle of dominance, solve the game whose pay-off matrix is given below:
Show that the set of vectors
from a basis for
The following table is obtained in the intermediate stage while solving an LPP by the simplex method. 
Discuss whether an optimal solution will exist or not.