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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?

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Solution Summary

Sensitivity analysis and LP solutions are examined in the solution. The different city warehouses are examined.

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LP in EXCEL Solver, Sensitivity Analysis and Limits Report

Acme Babyfoods mixes two strengths of apple juice. One quart of Beginner's juice is made from 30 fluid ounces of water and 2 fluid ounces of apple juice concentrate. One quart of Advanced juice is made from 20 fluid ounces of water and 12 fluid ounces of concentrate. Every day Acme has available 30,000 fluid ounces of water and 3,600 fluid ounces of concentrate. Acme makes a profit of 20 cents on each quart of Beginner's juice and 30 cents on each quart of Advanced juice. How many quarts of each should Acme make each day to get the largest profit? How would this change if Acme made a profit of 40 cents on Beginner's juice and 20 cents on Advanced juice?

You will be turning in two (2) deliverables, a short write-up of the project and the spreadsheet showing your work.

Write up:

Problem introduction

Write up the LP model for the problem. Include the objective function and all constraints, including any non-negativity constraints.

Present the optimal solution, based on your work in Excel. Explain what the results mean.

Write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.


As previously noted, please set up your problem in Excel and find the solution using Solver. Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.

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