Dibuat Diperiksa Mengetahui

Tanggal 14 Februari 2016 Tanggal 14 Februari 2016 Tanggal 14 Februari 2016 Oleh Yoka Fernando Oleh Annisa Fatma Magistra Oleh Angga Listio Jabatan Asisten Tutorial Jabatan Koordinator Tutorial OR 1 Jabatan Koordinator Asisten

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DEPARTEMEN PENDIDIKAN NASIONAL

UNIVERSITAS ANDALAS FAKULTAS TEKNIK

JURUSAN TEKNIK INDUSTRI LABORATORIUM PERENCANAAN DAN OPTIMASI SISTEM INDUSTRI

TUGAS PENDAHULUAN

OPERATIONAL RESEARCH 1

PROGRAM LINIER & METODE SIMPLEKS

1. My brother love steaks and potatoes. Therefore, he has decided to go on a steady diet

of only these two foods for all his meals. He realizes that this isn’t the healthiest diet,

so he want to make sure that he eats the right quantities of the two foods to satistfy

some key nutritional requirements. He has obtained the following nutritional and cost

information. Steak have 5% of carbohydrates, 20% of protein, and 15% of fat. And

then for potatoes have 15% of carbohydrate, 5% of protein, and 2% of fat. These

requirement ingredients consist more than 50 grams of carbohydrates and 40 grams of

protein and less than 60 grams of fat. So, my brothers want to determine minimum the

number of daily serving of potatoes and steak if the cost of serving for steak is $4 and

for potatoes is $2. The questions are:

a. What is linier programming in this situation?

b. Formulate a linier programming model for this problem !

c. Use the graphical method for this problem !

d. Do you think your answer is optimum? why? give your reason for this state !

2. Consider the following problem, you should solve this situation of linier

programming if, Maximize Z = 5x1 + 3x2 + 4x3, with constrains of situation :

2x1 + x2 + x3 ≤ 20

3x1 + x2 + 2x3 ≤ 30

Create your optimum solution for this problem !

Dibuat Diperiksa Mengetahui

Tanggal 14 Februari 2016 Tanggal 14 Februari 2016 Tanggal 14 Februari 2016 Oleh Yoka Fernando Oleh Annisa Fatma Magistra Oleh Angga Listio Jabatan Asisten Tutorial Jabatan Koordinator Tutorial OR 1 Jabatan Koordinator Asisten

TandaTangan

TandaTangan

TandaTangan

DEPARTEMEN PENDIDIKAN NASIONAL

UNIVERSITAS ANDALAS FAKULTAS TEKNIK

JURUSAN TEKNIK INDUSTRI LABORATORIUM PERENCANAAN DAN OPTIMASI SISTEM INDUSTRI

3. The area of parking 1,760 m2. Wide average - average of a small car 4 m2 and 20 m2

large car. The maximum capacity parking’s area are only 200 vehicles, the parking

cost of a small car is Rp.1.000,00 / hours and a large car Rp. 2000.00 / hours. If within

one hour fully charged and no vehicles were going and coming, the maximum yield of

the parking lot is ....?

4. Find the feasible region and the optimal solution of the following L.P.P:

Max Z= 5x1+ 4x2

s/t

2x1+ 4x2 ≤ 8

2x1 + x2 ≤ 2

3x2 ≤ 9

4x1+ x2 ≤ 4

x1,x2 ≥ 0

5. Use simplex method to solve the following linear programming problem (L.P.P).

Max Z = 12x1+ 8x2

Sub. To

8x1 +6x2 ≤ 2200

4x1+9x2 ≤ 1800

x1+ 2x2 ≤ 400

x1,x2 ≥ 0

6. Use simplex method to solve the following linear programming problem (L.P.P). Min

Min. Z = x1-3x2-2x3

Dibuat Diperiksa Mengetahui

Tanggal 14 Februari 2016 Tanggal 14 Februari 2016 Tanggal 14 Februari 2016 Oleh Yoka Fernando Oleh Annisa Fatma Magistra Oleh Angga Listio Jabatan Asisten Tutorial Jabatan Koordinator Tutorial OR 1 Jabatan Koordinator Asisten

TandaTangan

TandaTangan

TandaTangan

DEPARTEMEN PENDIDIKAN NASIONAL

UNIVERSITAS ANDALAS FAKULTAS TEKNIK

JURUSAN TEKNIK INDUSTRI LABORATORIUM PERENCANAAN DAN OPTIMASI SISTEM INDUSTRI

Sub. To

3x1 -x2+2x3 ≤ 7

-2x1+4x2 ≤ 12

-4x1+3x2+8x3 ≤ 10

x1,x2,x3 ≥ 0