Question #145131
four companies viz. W,X,Y, and Z supply the requirements of three warehouse viz. A, B, and C respectively. the companies availability, warehouse requirements and the unit cost of transporatation are given in the following table. find an initial basic feasible solution using
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Expert's answer
2020-11-23T11:03:08-0500

Let's Supply is SA,SB,SCS_A, S_B, S_C for all warehouse.

Let's Requirement is RW,RY,RX,RZR_W, R_Y, R_X,R_Z for all factories .

Since RY+RZ=SCR_Y +R_Z=S_C so the given problem is a degeneracy problem.

Now we will solve the transportation problem by Matrix Minimum Method.

To resolve degeneracy, we make use of an artificial quantity(d). The quantity d is so small that it does not affect the supply and demand constraints. Degeneracy can be avoided if we ensure that no partial sum of si(supply) and rj (requirement) are the same.

Substituting d=0.d=0.

Degeneracy has been removed

Answer=k1RW+k2(SARW)+k3SB+k4RYAnswer = k_{1}R_W+ k_{2}(S_A-R_W)+k_{3}S_B+k_{4}R_Y

where k1k_1 is a coefficient for RWR_W and SAS_A (from table)

k2k_2 is a coefficient for RXR_X and SAS_A (from table)

k3k_3 is a coefficient for RXR_X and SBS_B (from table)

k4k_4 is a coefficient for RYR_Y and SCS_C (from table)


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