|
|
Bullco
blends silicon and nitrogen to produce two types of fertilizers. Fertilizer 1 must be at least 40% nitrogen
and sells for $70/pound. Fertilizer 2
must be at least 70% silicon and sells for $40/lb. Bullco can purchase up to 80 lbs of
nitrogen at $10/lb and up to 100 lbs silicon at $15/lb. Assuming that all fertilizer produced can
be sold, formulate an LP to help Bullco maximize its profits. |
|
|
|
(From Introduction to
Mathematical Programming, by Wayne L. Winston. P.87) |
|
|
|
|
|
|
|
Formulate the Problem: |
|
|
|
Let
Xs1 be the amount in pounds of silicon used in fertilizer 1 and Xs2
be the amount in pounds of silicon used in fertilizer 2. Let Xn1 be the amount in pounds
of nitrogen used in fertilizer 1 and Xn2 be the amount in pounds
of nitrogen used in fertilizer 2. |
|
|
|
|
|
|
|
Objective
Function: |
|
|
|
Max
Z = 70(Xn1 + Xs1) + 40(Xn2+Xs2) – 15(Xs1 + Xs2) – 10(Xn1+Xn2) |
|
|
|
ST : Xs1 + Xs2 <= 100 |
|
|
|
Xn1 + Xn2 <= 80 |
|
|
|
Xn1
>= 0.4(Xs1 + Xn1) |
|
|
|
Xs2 >= 0.7(Xs2 + Xn2) |
|
|
|
All variabless >= 0 |
|
|
|
|
|
|
|
We need to convert these equations into equations that we can plug into Excel & Solver: |
|
|
|
Max
Z = 60Xn1 + 55Xs1 + 30Xn2 + 25Xs2 |
|
|
|
ST
: 1Xs1 + 1Xs2 <= 100 |
|
|
|
1Xn1 + 1Xn2 <= 80 |
|
|
|
0.6 Xn1 – 0.4Xs1 >= 0 |
|
|
|
0.3 Xs2 – 0.7Xn2 >= 0 |
|