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