x equals Banyak space roti space straight A y equals Banyak space roti space straight B
Dari soal dapat dituliskan ke dalam tabel berikut.
Penulisan model matematika
Fungsi kendala
table attributes columnalign right center left columnspacing 0px end attributes row cell 50 x plus 100 y end cell less or equal than cell 3.500 left right double arrow x plus 2 y less or equal than 70 end cell row cell 60 x plus 20 y end cell less or equal than cell 2.200 left right double arrow 3 x plus y less or equal than 110 end cell row x greater or equal than 0 row y greater or equal than 0 end table
Fungsi tujuan
z equals x plus y
Penentuan titik potong masing-masing garis pembatas dengan sumbu koordinat seperti terlihat pada tabel berikut.
Titik potong antar garis pembatas
table row x plus cell 2 y end cell equals 70 row cell 3 x end cell plus y equals 110 end table open vertical bar table row cell cross times 3 end cell row cell cross times 1 end cell end table close vertical bar table row blank blank blank blank blank blank row cell 3 x end cell plus cell 6 y end cell equals 210 blank row cell 3 x end cell plus y equals 110 minus row blank blank cell 5 y end cell equals 100 blank end table 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 y space space space equals 20 space space space space space space space space space space space space space space space space space space space space
table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 20 end cell equals 110 row cell 3 x end cell equals cell 110 minus 20 end cell row cell 3 x end cell equals 90 row x equals 30 end table
Daerah himpunan penyelesaian
Penentuan nilai maksimum dengan uji titik pojok
table attributes columnalign right center left columnspacing 0px end attributes row z equals cell x plus y end cell row cell open parentheses 110 over 3 0 close parentheses end cell rightwards double arrow cell z equals 110 over 3 plus 0 equals 110 over 3 end cell row cell open parentheses 30 comma 20 close parentheses end cell rightwards double arrow cell z equals 30 plus 20 equals 50 end cell row cell open parentheses 0 comma 35 close parentheses end cell rightwards double arrow cell z equals 0 plus 35 equals 35 end cell end table
Dengan demikian jumlah kedua macam roti yang dapat dibuat paling banyak adalah 50
Jawaban:
Misalkan
x equals Banyak space roti space straight A y equals Banyak space roti space straight B
Dari soal dapat dituliskan ke dalam tabel berikut.
Penulisan model matematika
Fungsi kendala
table attributes columnalign right center left columnspacing 0px end attributes row cell 50 x plus 100 y end cell less or equal than cell 3.500 left right double arrow x plus 2 y less or equal than 70 end cell row cell 60 x plus 20 y end cell less or equal than cell 2.200 left right double arrow 3 x plus y less or equal than 110 end cell row x greater or equal than 0 row y greater or equal than 0 end table
Fungsi tujuan
z equals x plus y
Penentuan titik potong masing-masing garis pembatas dengan sumbu koordinat seperti terlihat pada tabel berikut.
Titik potong antar garis pembatas
table row x plus cell 2 y end cell equals 70 row cell 3 x end cell plus y equals 110 end table open vertical bar table row cell cross times 3 end cell row cell cross times 1 end cell end table close vertical bar table row blank blank blank blank blank blank row cell 3 x end cell plus cell 6 y end cell equals 210 blank row cell 3 x end cell plus y equals 110 minus row blank blank cell 5 y end cell equals 100 blank end table 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 y space space space equals 20 space space space space space space space space space space space space space space space space space space space space
table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 20 end cell equals 110 row cell 3 x end cell equals cell 110 minus 20 end cell row cell 3 x end cell equals 90 row x equals 30 end table
Daerah himpunan penyelesaian
Penentuan nilai maksimum dengan uji titik pojok
table attributes columnalign right center left columnspacing 0px end attributes row z equals cell x plus y end cell row cell open parentheses 110 over 3 0 close parentheses end cell rightwards double arrow cell z equals 110 over 3 plus 0 equals 110 over 3 end cell row cell open parentheses 30 comma 20 close parentheses end cell rightwards double arrow cell z equals 30 plus 20 equals 50 end cell row cell open parentheses 0 comma 35 close parentheses end cell rightwards double arrow cell z equals 0 plus 35 equals 35 end cell end table
Dengan demikian jumlah kedua macam roti yang dapat dibuat paling banyak adalah 50
Jadi, jawaban yang tepat adalah C
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