Blending
Mossy mountain coffee buys beans and blends them into house blends for re-sale in 1 pound bags
Beans
$/pound
Amount avalible from supplies
Brazil
2.00
110
Columbia
2.90
80
Mocha
2.75
70
Selling $ / pond
Maximum demand
Recipe
Special
6
100pounds
>40% Columbian, <30% mocha
Dark
5.25
100
<60% Brazilian, < 10% Columbian
Use LP to find the best blends and maximize profit this week.
Decision variables
Blending variables
Let Xij represent pounds of beans
i= B,C,M blended into
blend j= S,D
ie. Xbs, Xcs, Xms, Xbd, Xcd, Xmd
note that if we use everything we buy
B= Xbs + Xbd
B amount bought
Xbs + Xbd amount used
C= Xcs+ Xcd
M= Xms + Xmd
If we sell everything we make
S= Xbs + Xcs +Xms
D= Xbd + Xcd +Xmd
2) constriants
Limited supply ( B<110 ) Xbs + Xbd< 110
( C <80 ) Xcs+ Xcd < 80
( M < 70 ) Xms + Xmd < 70
Limited demand : Xbs + Xcs +Xms < 100
Xbd + Xcd +Xmd <100
Recipe constraints
Special >40 % Colombian Xcs > 40% ( total special made and sold
· Two approaches
· If we know exactly...