Question

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Answer 1

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9) ................ Mobil (x) ....... Truk (y) .......
Kardus ....... 40x ............... 30y ............. 480
Peti ............. 16x ................ 32y ............. 352
Sewa .......... 100.000x .... 150.000y ... ???? Minimum
Model Matematika (ada kata paling sedikit berarti tandanya : ≥)
1) 40x + 30y ≥ 480
4x + 3y ≥ 48
x = 0 => y = 16 ==> (0, 16)
y = 0 => x = 12 ==> (12, 0)
2) 16x + 32y ≥ 352
4x + 8y ≥ 88
x = 0 => y = 11 ==> (0, 11)
y = 0 => x = 22 ==> (22, 0)
TITIK POTONG
4x + 3y = 48
4x + 8y = 88
------------------ --
....... -5y = -40 => y = 8
4x + 3y = 48 => 4x + 3(8) = 48 => 4x = 24 => x = 6 ===> (6, 8)
Setelah digambar diperoleh titik sudutnya : (6, 8), (0, 16) dan (22, 0)
Substitusikan ke sewa : f(x, y) = 100.000x + 150.000y
(6, 8) => 100.000(6) + 150.000(8) = 1.800.000
(0, 16) => 100.000(0) + 150.000(16) = 2.400.000
(22, 0) => 100.000(22) + 150.000(0) = 2.200.000
Jadi biaya minimumnya = 1.800.000

10) ................. anggrek (x) ..... dahlia (y) ..........
Orang .......... 4x ...................... 10y .................... 580
Jumlah .......... x ....................... y ........................ 100
Sewa ............. 400.000x ...... 500.000y ....... ???? Minimum
Model matematika
1) 4x + 10y ≥ 580
2x + 5y ≥ 290
x = 0 => y = 58 ==> (0, 58)
y = 0 => x = 145 ==> (145, 0)
2) x + y ≥ 100
x = 0 => y = 100 ==> (0, 100)
y = 0 => x = 100 ==> (100, 0)
TITIK POTONG
x + y = 100 => 2x + 2y = 200
......................... 2x + 5y = 290
----------------------------------------- --
................................... -3y = -90 => y = 30
x + y = 100 => x + 30 = 100 => x = 70 ==> (70, 30)
Setelah digambar diperoleh titik sudutnya : (70, 30), (0, 100) dan (145, 0)
Substitusi ke sewa : f(x, y) = 400.000x + 500.000y
(70, 30) => 400.000(70) + 500.000(30) = 43.000.000
(0, 100) => 400.000(0) + 500.000(100) = 50.000.000
(145,0) => 400.000(145) + 500.000(0) = 58.000.000
Jadi biaya minimumnya = 43.000.000

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