Download - linear programming
Linear Program&
mathematical models
English for Math “Linear Program”
St Zulaiha Nurhajarurahmah1111040168
International Class Program . Mathematic Department.
Mathematics and Science Faculty. State University of Makassar.
2012.
Linear ProgramDefinition of linear
program
Mathematical modelsOptimal solution &
objective formExAmple
Example 1:
+Max total = 150 kg
Max weight300 kg
= Rp 1000/ons
= Rp 1500/onsHow much is the
biggest obtainable profit?!
The relevant mathematical model for this problem
x+y≤150, and x+3y≤300 ,x≥0, y≥0, The objective function is (1.000x+1.500y)
Y
X0
100150
150 300
(75,75)
Feasible region
Evaluate the value of the objective function at each of those points, as in the following:
Thus, the maximum profit of the merchant is Rp187.500,00
Point corner (x,y)(0,0)
(150,0)(75,75)(0,100)
f(x,y)=1.000x+1.500y1.000(0)+1.500(0)=0
1.000(150)+1.500(0)=150.0001.000(75)+1.500(75)=187.5001.000(0)+1.500(100)=150.000
Find the maximum profit...!
Example 2:
+ = Max 350 g
1 2
3 boxes + 5 boxes = max 1500 g
= Rp 200,00 = Rp 300,00
x+y≤350, and 3x+5y≤1500 ,x≥0, y≥0, The maximum of objective function (200x+300y)
What is the mathematical
model from that problem?
300350
500350
Y
0
(125,225)
FR
X
Thus, the fesible region like this:
To determine the optimum value and objective function by the ISO-Profit line method
300
350
500
350
Y
X0
k
(125,225)
Ax+By=k ; k=AB
than,z = f (x, y) = 200x + 300y
f (125,225) = 200(125) + 300(225)
= 25.000 + 67.500= 92.500
Thus, the maximum profit of the merchant is Rp 92.500,00
Thanks for ur attention