Blending problem
A manufacturer produces a feeding mix for dairy cattle. 
The feed mix contains two active ingredients and a filler to provide bulk. 
One kg of feed mix must contain a minimum quantity of each of four nutrients as below: 

Nutrient       A      B     C     D
gram           80     50    25    5

The ingredients have the following nutrient values and cost 

                        A      B       C       D      Cost/kg
Ingredient 1 (gram/kg)  100    50      40      10     40
Ingredient 2 (gram/kg)  200    150     10      -      60

What should be the amounts of active ingredients and filler in one kg of feed mix? 

solution is x1= 0.5905, x2=0.2364 and x3=0.2727.

Solve in R with:
require(LIM)
LIMBlending <- Setup("blending.input")
Linp(LIMBlending)
#######################################3

### COMPONENT
 
 pIngredient1   ! Part ingredient 1
 pIngredient2   ! Part ingredient 2
 pFiller        ! Part ingredient 3 = filler

### END COMPONENTS


### PARAMETERS

! Minimum Nutrient composition
 MinNutrientA = 80
 MinNutrientB = 50
 MinNutrientC = 25
 MinNutrientD = 5

### END PARAMETERS

### INEQUALITIES

 NutrientA : 100*pIngredient1 + 200*pIngredient2 > MinNutrientA
 NutrientB : 50*pIngredient1  + 150*pIngredient2 > MinNutrientB
 NutrientC : 40*pIngredient1  +  10*pIngredient2 > MinNutrientC
 NutrientD : 10*pIngredient1                     > MinNutrientD

### END INEQUALITIES 

### EQUALITIES

 Balance   : pIngredient1 + pIngredient2 + pFiller = 1

### END EQUALITIES

### COST

 40 * pIngredient1 + 60*pIngredient2

### END COST

