Linear Programming Problem by Graphing Method
2026-02-09 09:10
Tags: #math Author: Duke Hsu
Linear Programming Problem by Graphing Method
Solution Step
I - Decision Variable
Let
x= basket flower
y= bouquet flower
Find 2 variables in a given problem
II - Create a Table
For example:
| x | y | ||
|---|---|---|---|
| flower | 24 | 12 | <=600 |
| ribbon | 2 | 1 | <=90 |
| basket | 1 | - | <=30 |
| wrappers | - | 2 | <=60 |
| profit | 900 | 500 | need maximum |
Find the variable data through the given problem, and create a table.
III - Linear Programming Problem (LPP) Model
List LPP models via table
Object function
of maximum profit:
\(P = 900x + 500y\)
of minimum:
Subject to :
\(24x+12y \leq 600\)
\(2x+y\leq 90\)
\(x\leq30\)
\(2y\leq 60\)
IV - Graphing
Point A: (0,50), (25,0) Point B: (0,90),(45,0) Point C: (30,0) Point D: (0,30)
V - Conner Point
E: (10,30)
Computation:
\(P = 24x+ 12y\)
\(P = 900 \times 10 + 500 \times 30 = 24,000\)
VI - Conclusion
There are for
x=10 basket of flower
y=30 bouquet of flower