1. Disclaimer: This publication reflects only the author’s views and the European Commission and UK NA are not responsible for any use that may be made of the information it contains.

2. A Little Problem
James has to buy drinks for himself and 4 friends. He has £2.50 to spend.
A can of cola costs 60p
A can of orange costs 40p
He can buy x cans of Cola and y cans of Orange;
Explain why
(i) x + y  5
(ii) 6x + 4y  25
Write down all the different combinations of each type of drink he can buy.
1 coke + 4 Oranges
6 Oranges
2 coke + 3 Oranges
5 Oranges

3. What % of each should they buy?
A “Real-Life” problem
Price Farm Chickens in Hereford supply Sun Valley Foods with live chickens.
By law the chickens must be reared correctly according to strict dietry needs.
Obviously, the firm must keep costs as low as possible but must obey the law.
The law states that the chicks need the following:
No less than 20% protein
No less than 10 % fat
Exactly 50% Carbohydrate
No greater than 50% Fibre and Ash
The farm can buy the following ingredients with the following contents and cost;
Soya flour
50% prot, 20% fat, 20% carb, 10% F&A = £60 per ton
Meat Meal
50% prot, 10% fat, 0% carb, 40% F&A = £50 per ton
Enriched skimmed Milk
30% prot, 20% fat, 40% carb, 10% F&A = £70 per ton
Sago Flour
100% carb = £40 per ton
What % of each should they buy?

4. Linear Programming Modelling No! ……… Not that kind of modelling…
Mathematical Modelling!!!
A model is a way of building
a simulation of a real life
situation which we want to improve.
 R.Jones /05/07

5. Optimisation Examples
Linear Programming
Optimisation Examples
Battle Strategies
Blending Ingredients
Profit and Loss
Management of people or products
 R.Jones /05/07

6. We love Chicken Nuggets
The Problem
We love Chicken Nuggets
Our company supplies chicken nuggets to Superbites.
We need to ensure the chicks are fattened up before the
kill, it must be more than 10%.
We can feed them soya flour and powered milk.
Soya flour has 50% protein, 20% fat, 20% carb, 10% F&A.
Powdered milk has 30% protein, 10% fat, 0% carb, 40% F&A.
The chicks must have more than 50% protein, 10% fat, exactly 50%
Carbohydrate and no more than 50% F&A to be healthy.
They must eat a blend of milk and soya our they will be sick.
If Soya costs £60/ton and Milk costs £20/ton what percentage blend should we buy to spend the least?
 R.Jones /05/07

7. The A, B , Cs of Optimisation
Linear Programming
The A, B , Cs of Optimisation A
ADJUSTABLES (Things we can change) B
BEST (What we are trying to improve) C
CONSTRAINTS (The rules)
 R.Jones /05/07

8. The A, B , Cs of Optimisation
Linear Programming
The A, B , Cs of Optimisation
Adjustables :
X = tonnes of Soya Flour
y = tons of Powered Milk per day
Best :
Min Cost = 60 x + 20y
Constraints :
Protein
0.5x + 0.3y  0.5
 5x + 3y  5
Fat
0.2x + 0.1y  0.1
 2x + y  1
x  0
y  0
Carbohydrate
0.2x = 0.5
 x = 2.5
Fibre & Ash
0.1x + 0.4y  0.5
 x + 4y  5
 R.Jones /05/07

9. Answer here (but decimal!!)
Better here (why)
Plot Objective Function line
0.5x+y = £50