Pemrograman Linier (Sistem Pendukung Keputusan)

 

Fungsi Tujuan :

Z = 200x + 100y

Fungsi Kendala :

(i)                  8x + 7y <= 56

(ii)                5x + 12y <= 60

Menentukan titik potong

(i)                  Jika x = 0                      Jika y = 0

8(0) + 7y = 56                             8x + 7(0) = 56

           7y = 56                               8x   = 56

            y  = 56/7                             x   = 56/8

            y = 8                                   x = 7

    (0,8)                                                   (7,0)

(ii)                Jika  x = 0                     jika y =0

5(0) + 12y = 60           5x + 12(0) =60

           12y = 60             5x   = 60

                Y = 60/12      x     = 60/5

               Y = 5               x = 12

             (0,5)                                  (12,0)

 

A ( 0,5)

B ( 4.1, 3.3)

C (7,0)

8x + 7y   = 56  x5  40x + 35y  = 280

5x + 12y = 60  x8  40x + 96y  = 480

                                          -61y = -200

                                                   Y  = 200/61

                                               Y  = 3,3

8x + 7 (3,3) = 56

8x + 23,1 =56

8x             = 56 – 23,1

8x             =   32,9

X               =  32,9/8

X               =  4,1

A = 200(0) + 100(5)                     Yang paling menguntungkan adalah solusi C

   = 500

B = 200(4.1) + 100(3.3)

   = 820 + 330

  = 1150

C = 200 (7) + 100(0)

   =  1400