CONFIDENTIAL.

QUESTION $4$

Poge sof?

a$.$ What is the general transportation problem concerned with?

b$.$ Describe the cost ausumption for the transportation problem.

c$.$ The transportation problem is a special type of $1$ P problem. Which assumption $($other than the cost assumption$)$ must hold so that an L$.$P problem may be formulated as a transportation problem$)?$

d$.$ Consider the transportation problem having the following parameter table:

Answer this question on the answer sheet provided.

$\backslash$table$[[,,$Destination$],[,,1,2,3,4,5,6,$Supply$],[$Source$,1,13,10,22,29,18,0,5],[2,14,13,16,21,40,0,6],[3,3,0,M,11,6,0,7],[4,18,9,19,23,11,0,4],[,5,30,24,34,36,28,0,3],[$Demand$,3,5,4,5,6,2,]]$

i$.$ Use Vogel's approximation method to obtain an initial Basic Feasible solution.

ii$.$ Given the following BF solution to the problem: $x_{96}=2$;$x_{31}=3$;$x_{34}=4$;$x_{12}=5$; $x_{15}=4$;$x_{55}=1$;$x_{22}=0$;$x_{23}=4$;$x_{24}=1$;$x_{25}=1.$

Use the optimality test to show that this solution is not optimal.

Hint: Let $t_2=0.$

iii. Using the initial BF solution given in question $($ii$),$ perform the next iteration $($only$)$ of the transportation simplex method.