Geogebra Plus Linear Programming

We’ll Create a Geogebra program to help us with our linear programming — #PySeries#Episode 02

First, we’ve got this problem that comes from the math to your course guide from the Pingree school.

It is the tape’s verse CDs example:

Suppose you want to buy some tapes and CDs. Does anyone really buy tapes anymore? Anyway, you can buy up to 11 tapes; You can buy up to 7 CDS, but you want at least 3; You must get enough tapes or CDs to hold at least 10 hours of music; Each tape holds about 45 minutes of music and each CD holds an hour a tape costs $8 and a CD costs $12; So how many tapes and CDs should you buy to minimize your cost?

Let’s see the solution using Geogebra than in the end I will present the Python solution.

1# Define Your Variables:

x=The number of tapes to buy;
y=The number of CDs to buy;

2# Translate your constraints:

x<=11
3<=y>=7
600<=45x+60y

3# Type your objective Function:

T(x,y)=8x+12y

4# Open a Geogebra New Activity session, Hit Geogebra, Create an Applet and get a name to your applet (mine is GeoPlusLinearProg):

You can expand the applet according to your screen resolution:

Just fine!

5# On Geogebra, on the left, type the inequality as well as equality like this:

a: x <= 11
b: x  = 11
c: 3 <= y <= 7
d: y  = 3
e: y  = 7
f: 45*x + 6*y >= 600
g: 3*x + 4*y = 40

The regions in the graph are presented, now configure them according to your taste, clicking on each inequality and changing the style and color properties. Here are my settings.

6#Now, click Point > Intercept and create 4 points, in the region of interest:

7# On Geogebra, open a Spreadsheet and type (hamburger icon>View>Spreedsheet located at top-right):

Now, in the spreadsheet type this (drag the little rectangle down):

Points - Total Cost, T
A   =8*x(A2)+12*y(A2)
B   =8*x(A3)+12*y(A3)
C   =8*x(A4)+12*y(A4)
D   =8*x(A5)+12*y(A5)

Any of the vertices of the trapeze serve as an answer. I choose the second option(9 Tapes and 3 CDs).

Let’s see what python decides …

8# Python Solution:

from pulp import *
prob=LpProblem('Example', LpMaximize)
x1=LpVariable("Tape", 0)
x2=LpVariable("CD", 0)
prob += x1<=11
prob += x2>=3
prob += x2<=7
prob += 45*x1+60*x2<=600
prob += 8*x1+12*x2
prob.solve()
for v in prob.variables():
    print(v.name,"=", v.varValue)
print("Total Cost = ", value(prob.objective))

CD = 7.0 
Tape = 4.0 
Total Cost =  116.0

# Episode 01 #PySeries # An overview of the Opportunities Offered by Python in Engineering

And that’s all for now!

I hope you were impressed with the Geogebra app like I am!

Bye for now!

See you in the next episode of Python Series!

https://docs.google.com/document/d/1DkycafWLUZeprvnTQcSgaasyniTWTeDe4cEzEnN6hes/edit?usp=sharing

References & Credits

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