# Linear Programming - Transportation Problem, NW corner

3. Emily Alice PLC is a printing company which specializes in the design and production of special effect booklets for marketing promotions. A new client orders 60,000 booklets which are to be sent to their offices in London, Manchester and Newcastle. These offices require 15000, 21000 and 24000 copies respectively.

Each of its printing works at Hill and Bath can produce up to 35,000 copies by the deadline. Given the following table of transportation costs (in pence per booklet), determine how many copies should be produced at Hull and at Bath and how should these be distributed if the total transportation cost is to be minimized.

London Manchester Newcastle

Hull 8 7 4

Bath 4 6 7

Use the North-West corner method to find the first basic feasible solution and state the minimum transportation cost.

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#### Solution Preview

Because, total demand (= 60,000) < total supply (= 70,000)

Hence, a dummy demand column to be created with cost = 0

London (C1) Manchester (C2) Newcastle (C3) Dummy (C4) Supply

Hull (R1) 8 7 4 0 35,000

Bath (R2) 4 6 7 0 35,000

Requirements 15,000 21,000 24,000 10,000 Total=70,000

Start allocating from North-West corner, i.e., with (R1,C1): Minimum of C1_requirements(=15,000) and R1_supply(=35,000) = 15,000.

Hence, maximum possible units that can be allocated to R1,C1 = 15,000, allocate it. Hence remainder(C1_requirements ) = 0; remainder(R1_supply) = 35,000 - 15,000 = 20,000. Strike-off remaining cells of C1.

London (C1) ...

#### Solution Summary

Using North-West corner method, a Linear programming problem is solved here.