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# Sensitivity Analysis and LP solve

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Transportaton Problem (Minimal Cost)

There are three warehouses at different cities: Tauranga, Wanganui and Wellington. They have 180, 100 and 150 tons of paper available over the next week respectively. There are four publishers in Auckland, Palmerston North, Hamilton and Wellington. They have ordered 190, 70, 120 and 50 tons of paper for the next week. The costs in dollars of transportation of one ton of paper are given in the following table:

From/To Auckland Palmerston North Hamilton Wellington
Tauranga 21 42 11 54
Wanganui 45 7 33 11
Wellington 67 14 30 1

a) Formulate this problem as an LP solve using Solver in Excel
b) From the sensitivity analysis, which warehouse site should have had more paper allocated to it at the start of the week and by how much per tonne would the overall cost of transport have been reduced?
c) How much more paper could have been allocated to this warehouse without having to resolve the LP problem?
d) Instead of using road transport from Wellington to Auckland, it has been proposed that shipping the paper might be an alternative. Work out what price the shipping company would have to meet in order for you o have to re-run your LP to find a new optimum solution
e) If you had the option of hanging the distribution of paper stored in the Warehouses, what distribution would you have started the week with?