Transportation and Assignment

A Company has 2 production facilities S₁ and S₂ with production capacity of 100 and 110 units per week of a product, respectively. These units are to be shipped to 3 warehouses D₁, D₂ and D₃ with requirement of 80, 70 and 60 units per week, respectively. The transportation costs (in $) per unit between factories to warehouses are given in the table below:

Sources \ Destination	D₁	D₂	D₃	Supply
S₁	1	2	3	100
S₂	4	1	5	110
Demand	80	70	60

Find initial basic feasible solution to the above transportation problem using North West Corner Method, then optimize the solution.

The assignment cost of assigning any one operator to any one machine is given in the following Table:

Machines \ Operators	I	II	III	IV
A	10	5	13	15
B	3	9	18	3
C	10	7	3	2
D	5	11	9	7

Find the optimal assignment.

Find the values of $p$ and $q$ which will render the entry (2, 2) a saddle point for the game:

$$Player\ B$$
$$Player\ A \begin{bmatrix} 2 & 4 & 5 \ 10 & 7 & q \ 4 & p & 6 \end{bmatrix}$$

Solve the following LP problem using simplex method
Minimize $z = 10x_1 + 15x_2 + 20x_3$
Subject to $2x_1 + 4x_2 + 6x_3 \leq 24$
$3x_1 + 9x_2 + 6x_3 \leq 30$
$x_1, x_2, x_3 \geq 0$

Solve the following transportation problem using Northwest corner cell method and Least cost cell method.

	Destination 1	Destination 2	Destination 3	Destination 4	Supply
Source 1	3	1	7	4	300
Source 2	2	6	5	9	400
Source 3	8	3	3	2	500
Demand	250	350	400	200	1200

Solve the TSP as to minimize the cost per cycle.

From \ To	1	2	3	4	5
1	$\infty$	10	25	25	10
2	1	$\infty$	10	15	2
3	8	9	$\infty$	20	10
4	14	10	24	$\infty$	15
5	10	8	25	27	$\infty$

For the game with pay off matrix

Player A \ Player B	1	2	3
1	-1	2	-2
2	6	4	-6