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Pertanyaan

Sebuah pabrik memproduksi tiga jenis barang, yaitu barang A, barang B, dan barang C. Banyak barang yang diproduksi untuk masing-masing jenis barang dan biaya produksi perhari selama tiga hari pertama diperlihatkan pada tabel berikut:



 

Misalkan biaya produksi persatuan barang konstan. Pada hari ke-4 diproduksi sebanyak 20 unit barang A, 30 unit barang B, 35 unit barang C. Berapa biaya produksi total pada hari ke-4 itu?

  1. Rp13.000space 

  2. Rp130.000space 

  3. Rp210.000space 

  4. Rp310.000space 

  5. Rp380.000space 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Misalkan:

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell biaya space produksi space per space unit space barang space straight A end cell row y equals cell biaya space produksi space per space unit space barang space straight B end cell row z equals cell biaya space produksi space per space unit space barang space straight C end cell end table 

Maka, model matematika sistem persamaan linear tiga variabel (SPLTV) dari masalah di atas adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 20 x plus 10 y plus 5 z end cell equals cell Rp space 140.000 comma 00 end cell row cell 4 x plus 2 y plus z end cell equals cell Rp space 28.000 comma 00 space... space left parenthesis 1 right parenthesis end cell row blank blank blank row cell 10 x plus 10 y plus 10 z end cell equals cell Rp space 130.000 comma 00 end cell row cell x plus y plus z end cell equals cell Rp space 13.000 comma 00 space... space left parenthesis 2 right parenthesis end cell row blank blank blank row cell 5 x plus 10 y plus 15 z end cell equals cell Rp space 140.000 comma 00 end cell row cell x plus 2 y plus 3 z end cell equals cell Rp space 28.000 comma 00 space... space left parenthesis 3 right parenthesis end cell end table   

Eliminasi persamaan (1) dan (2):

4 x plus 2 y plus z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 28.000 comma 00 bottom enclose x plus y plus z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 13 end table.000 comma 00 space minus end enclose space space space space space space space space space space 3 x plus y equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 15.000 comma 00 space... space left parenthesis 4 right parenthesis  

Eliminasi persamaan (2) dan (3):

space space space space space space x plus y plus z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 13.000 comma 00 space open vertical bar cross times 3 close vertical bar 3 x plus 3 y plus 3 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 39.000 comma 00 space space x plus 2 y plus 3 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 28.000 comma 00 space open vertical bar cross times 1 close vertical bar space space bottom enclose x plus 2 y plus 3 z equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 28.000 comma 00 space minus end enclose space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 x plus y equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 11 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 000 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 00 end table space... space left parenthesis 5 right parenthesis  

Eliminasi persamaan (4) dan (5):

3 x plus y equals Rp space 15.000 comma 00 bottom enclose 2 x plus y equals Rp space 11.000 comma 00 space minus end enclose space space space space space space space space space x equals Rp space 4.000 comma 00  

Substitusi x equals Rp space 4.000 comma 00 ke persamaan (5):

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus y end cell equals cell Rp space 11.000 comma 00 end cell row cell 2 left parenthesis Rp space 4.000 comma 00 right parenthesis plus y end cell equals cell Rp space 11.000 comma 00 end cell row cell Rp space 8.000 comma 00 plus y end cell equals cell Rp space 11.000 comma 00 end cell row y equals cell Rp space 11.000 comma 00 minus Rp space 8.000 comma 00 end cell row y equals cell Rp space 3.000 comma 00 end cell end table  

Substitusi x equals Rp space 4.000 comma 00 dan y equals Rp space 3.000 comma 00 ke persamaan (2):

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y plus z end cell equals cell Rp space 13.000 comma 00 end cell row cell Rp space 4.000 comma 00 space plus Rp space 3.000 comma 00 plus z end cell equals cell Rp space 13.000 comma 00 end cell row cell Rp space 7.000 comma 00 plus z end cell equals cell Rp space 13.000 comma 00 end cell row z equals cell Rp space 13.000 comma 00 minus Rp space 7.000 comma 00 end cell row z equals cell Rp space 6.000 comma 00 end cell end table  

Maka, biaya produksi pada hari keempat adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell 20 x plus 30 y plus 35 z end cell equals cell 20 open parentheses Rp space 4.000 comma 00 close parentheses plus 30 open parentheses Rp space 3.000 comma 00 close parentheses plus 35 open parentheses Rp space 6.000 comma 00 close parentheses end cell row blank equals cell Rp space 80.000 comma 00 plus Rp space 90.000 comma 00 plus Rp space 210.000 comma 00 end cell row blank equals cell Rp space 380.000 comma 00 end cell end table  

Jadi, total biaya produksi pada hari keempat adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank Rp end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 380 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 000 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 00 end table.

Dengan demikian, jawaban yang tepat adalah E.

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