For political reason outside the control of the company paint factory C must supply a minimum of 350m3 to Elgy Autos.
What is the optimum amount of paint each factory should supply to each car manufacturing plant and what is the minimum cost of paint to the car manufacturer? As a note in the real world such an analysis is only the starting point. Sensitivity analysis would follow as well as some scenario planning such how much extra does the political constraint cost.

The Second Part

Once again involves the paint supply company and Elgy Autos.

The Problem

Elgy Autos has told the paint company that it needs to have representatives from the paint company on each of its sites: in the UK (plant 2), France (plant 1) and the Czech Republic (plant 3) to supervise the application of its paint to Elgy Autos motor cars. Elgy Autos have instructed the paint company that it does not care how many representatives are on site but they must cover the following skills:

• At least one of its representatives must speak the local language
• At least one of the representatives must be able to do colour matching. That is making sure that each car and part of a car meets the colour specifications. This is actually a highly skilled job that needs lots of experience to do.
• At least one of the representatives must be able to do quality control, ie the paint viscosity must be correct, the adhesion must be correct, others factors such as orange pealing must not exist on the paint. Once again this is a highly skilled job.
The paint company has also decided that one of the representatives must
• Be able to deal with the logistics of supplying paint: it wants to maintain minimum stock levels on site yet if they run out of paint the production line must stop and would result in a fine of a million euros a day, which naturally it wants to avoid by having an experienced logistics manager on site.

All we are interested in here is to have a logistics expert on site
The company has 8 candidates with various skills and associated costs of employing them in different locations. The task the paint company faces is which employees to place in each paint plant to meet the constraints and minimise the costs. Most potential representatives have more than one skill and more than one language so it may be possible to have only two representative at one plant, which will result in considerable savings for the company. No employee can work in more than one country.
The cost of employing each candidate representative in each country is given below in euros per annum.

France UK Czech Republic
Tinker 89100 99000 72000
Tailor 82800 118700 64700
Soldier 109300 107000 63100
Sailor 110100 73800 65200
Richman 72200 98900 54300
Poorman 71800 785000 63700
Beggarman 106100 116300 66700
Thief 90000 93700 64700

The language spoken by each representative are:

Tinker English Czech
Tailor English French
Soldier Czech English
Sailor English
Richman English
Poorman English
Beggarman English French
Thief Czech English

The skills each representative have are:

Tinker Quality Control Logistics
Tailor Logistics Quality Control
Soldier Quality Control
Sailor Colour Matching Quality Control
Richman Logistics Colour Matching
Poorman Quality Control Colour Matching
Beggarman Quality Control Colour Matching
Thief Colour Matching Quality Control

What you are required to do

You are to write a script in Matlab (a .m file) to solve the problem and submit the script to me along with any other tools you have used such as excel spreadsheets to solve this problem. You must also state clearly who is to work where and what it will cost.

It is possible that there is no combination of people that meet all the requirements. This happens in real life as well. If this happens for your set of employees sent me all your scripts and matrices and I will modify the skill sets/ languages of your candidates to get a feasible solution.

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