SOAL SPK

    1.  Rangkuman Informasi kedalam Tabel

Produk	Tenaga Kerja (jam/unit)	Tanah liat (kg/unit)	Laba
Mangkok	1	3	4000
Cangkir	2	2	5000

Misalkan :

                X = Mangkok

                Y = Cangkir

                Z = Laba

  

2.    2.   Menentukan Fungsi

·         Fungsi tujuan = misalkan z= 4000x + 5000y

·         Fungsi kendala = fungsi mangkok = 1x + 3y ≤ 4000

= Fungsi cangkir = 2x + 2y ≤ 5000 

      3.  Menentukan titik potong

-          Mangkok = 1x + 3y = 4000                   

X = 0                                                              y = 0

1(0) + 3y = 4000                                         1x + 3(0) = 4000

           3y = 4000                                                          1x= 4000

             Y = 1.3                                                                x= 4000

                        (0,1)                                                                       (4000,0)

-          Cangkir = 2x + 2y = 5000                        y=0

X=0                                                        2x + 2(0)= 5000

2(0) + 2y = 5000                                                 2x = 5000

                2y=5000                                                 x=2500

                  Y= 2500                                                               (2500,0)

                                (0,2500)

     4.  Eleminasi kedua persamaan fungsi kendala :

1x + 3y =4000           2

2x + 2y = 5000          1

2x + 6y = 8000

2x + 2y = 5000

                         4y = 3000

                           Y = 750

                         Substitusi ke pers (1)

                         1 *750 + 3y =4000

                                750 + 3y = 4000

                                           3y = 4000-750

                                                3y= 3250

                                                Y= 1083

5.       Subsitusi ke titik koordinat ke dalam

persamaan fungsi tujuan = z = 4000x + 5000y

titik A (0,0) z = 4000 (0) + 5000 (0)

                                = 0

Titik B (4000,0)z = 4000 (4000)+ 5000 (0)

                                = 160.000.00

Titik C (0,2500)z = 4000 (0) + 5000 (2500)

                                = 125.000.00

Grafik

               y

      2500 ●(0,2500)

       2000

       1000

         500

         200

         100                                                                                (2500,0)

              1●(0,1)                                                                           ●                      ●                x

             0 ●     20  40  60  100  150  200  1000  2000  2500 3000 4000 4500

                                                                                                                              (4000,0)