Operations research UE Past Papers Questions.

Using some economic theories, briefly explain the following

1. The coefficient of slack variables equal zero in the objective function
2. The basic variables in the initial simplex tableau are the slack variables
3. In the simplex method of solving L.P problem, the variable with the largest positive value is the entering variable. Give its economic rationale.

Answer / Solution

UNSOLVED

The HC & AC Ltd makes two kinds of tables-end tables(X1) and coffee tables(X2). The manufacture is restricted by material and labor constraints, as shown in the following linear programming formulation.

Maximize

Subject to

The final optimal simplex tableau for this problem is as follows:

			200	300	0	0
	Basic variables	Quantity	X1	X2	S1	S2
300	X2	30	0	1	1/3	-2/9
200	X1	15	1	0	-1/3	5/9
		12,000	200	300	100/3	400/9
	-		0	0	-100/3	-400/9

1. Formulate the dual for this problem
2. Prove that the shadow price for labor hour is $100/3
3. What is the importance of the duality theory to the agribusiness managers?

Answer / Solution

UNSOLVED

1. Why do waiting lines form at a service facility even though there may be more than enough service capacity to meet normal demand in the long run?
2. What are the assumptions and limitations of the Queuing theory?

Answer / Solution

UNSOLVED

1. Using vivid examples , distinguish between a transportation model and assignment model.
2. A concrete company transports concrete from three plants to three construction sites. The supply capacities of the three plants, the demand requirements at the three sites and the transportation costs per ton are as follows.

Determine the linear programming model formulation for this problem and find the initial optimal solution using the Minimum Cost (MCC) method.

Answer / Solution

UNSOLVED

Briefly describe the management science approach to problem solving.

Answer / Solution

UNSOLVED