Solve the following LP problem by using two-phase simplex method:
To solve this Linear Programming (LP) problem using the Two-Phase Simplex Method, follow these steps: ### Step 1: Formulation of the Problem The given LP problem is: \[ \text{Minimize } z = x_1 - 2x_2 - 3x_3 \] Subject to: \[ -2x_1 + 3x_2 + 3x_3 = 2 \] \[ 2x_1 + 3x_2 + 4x_3 = ______ _________ ___ ______ ________ __________ ______.
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Using the initial basic feasible solution for the transportation problem given below, find and optimal solution for the problem.
Find an initial basic feasible solution for the following transportation problem using matrix-minima method. Also find the transportation cost.
Solve, graphically, the game whose pay-off matrix is:
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.
Test the following set for convexity.
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:
The initial basic feasible solution of a transportation problem is given below:
Check whether the given solution is optimal. If it is not, then find the optimal solution.