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Question 1:The manufacturer can make a maximum profit of Rs.

[2011]

Question 2:A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only.The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximizationof profits, the daily production quantities of P and Q toys should respectively be

[2004]

Question 3: Simplex method of solving linear programming problem uses

[2010]

Question 4:The dual for the LP in Q. 21 is

[2008]

Question 5:After introducing slack variables s and t, the initial basic feasible solution is represented by the table below (basic variables are s = 6 and t = 6, and the objective function value is 0).

After some simplex iterations, the following table is obtained

From this, one can conclude that

After some simplex iterations, the following table is obtained

From this, one can conclude that

[2008]

Question 6:For the standard transportation linear program with m sources and n destinations and total supply equaling total demand, an optimal solution (lowest cost) with the smallest number of non-zero xij values (amounts from source i to destination j) is desired. The best upper bound for this number is

[2008]

Question 7:For the linear programming problem:

Maximize z = 3x_{1} + 2x_{2}

Subject to –2x_{1} + 3x_{2} < 9x_{1} – 5x_{2} > – 20x_{1}, x_{2} > 0

The above problem has

Maximize z = 3x

Subject to –2x

The above problem has

[2016]

Question 8:Maximize z = 15x_{1} + 20x_{2}

Subject to 12x_{1} + 4x_{2} > 36

12x_{1} + 6x_{2} > 24 x_{1},

x_{2} > 0

The above linear programming problem has

Subject to 12x

12x

x

The above linear programming problem has

Question 9:A linear programming problem is shown below:

Maximise 3x + 7y

Subjeot to 3x + 7y < 10

4x + 6y < 8 x, y > 0

Maximise 3x + 7y

Subjeot to 3x + 7y < 10

4x + 6y < 8 x, y > 0

[2013]

Question 10:The manufacturer can make a maximum profit of Rs.

[2011]

Question 11:One unit of product P1 requires 3 kg of resource R_{1} and 1 kg resource R_{2}. One unit of product P_{2} requires 2 kg of resource R_{1} and 2 kg of resource R_{2}. The profits per unit by selling product P1 and P2 and Rs. 12000 and Rs 3000 respectively. The manufacturer has 90 kg of resource R_{1}, and 100 kg of resource R_{2.}

The unit worth of resource R_{2}, i.e. dual price of resource R_{2} in Rs per kg is

[2011]

Question 12:Consider the following Linear Programming Problem (LPP):

Maximize z = 3x_{1} + 2x_{2},

Subject to x_{1} < 4 x_{2 }< = 6

3x_{1} + 2x_{2} < 18

x_{1} > 0, x_{2} > 0

Maximize z = 3x

Subject to x

3x

x

[2009]

Question 13:A firm is required to procure three items (P, Q, and R). The prices quoted for these items (in Rs.) by suppliers S1, S_{2 }and S_{3} are given in table. The management policy requires that each item has to be supplied by only one supplier and one supplier supply only one item.The minimum total cost (in Rs.) of procurement to the firm is

[2006]

Question 14:Let Y1 and Y2 be the decision variables of the dual and v1 and v2 be the slack variables of the dual of the given linear programming problem.The optimum dual variables are

[2005]

Question 15:If an additional constraint X_{1} + X_{2} < 5 is added, the optimal solution is

[2005]

Question 16:A company has two factories S_{1}, S_{2} and two warehouses D_{1}, D_{2}. The supplies from S_{1} and S_{2} are 50 and 40 units respectively. Warehouse D_{1} requires a minimum of 20 units and a maximum of 40 units. Warehouse D_{2} requires a minimum of 20 units and, over and above, it can take as much as can be supplied. A balanced transportation problem is to be formulated for the above situation. The number of supply points, the number of demand points, and the total supply (or total demand) in the balanced transportation problem respectively are

[2005]

Question 17:A component can be produced by any of the four processes, I, II, III and IV. Process I has fixed cost of Rs. 20 and variable cost of Rs. 3 per piece.Process II has a fixed cost of Rs. 50 and variable cost of Rs. 1 per piece. Process III has a fixed cost of Rs. 40.00 and variable cost of Rs. 2 per piece. Process IV has fixed cost of Rs. 10 and Variable cost Rs. 4 per piece. If company wishes to produce 100 pieces of the component, from economic point of view it should choose

[2005 : 2 Marks]

Question 18:A manufacturer produces two types of products, 1 and 2, at production levels of x_{1} and x_{2} respectively. The profit is given is 2x_{1} + 5x_{2}. The production constraints are:

x_{1} + 3x_{2} < 40

3x1 + x_{2} < 24

x_{1} + x_{2} < 10

x_{1} > 0 x_{2} > 0

The maximum profit which can meet the constraints is

x

3x1 + x

x

x

The maximum profit which can meet the constraints is

[2003]

Question 19:If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that

[1996]

Question 20:In an assembly line for assembling toys, five workers are assigned tasks which take times of 10, 8, 6, 9 and 10 minutes respectively. The balance delay for line is

[1996]

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