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Seorang pedanagan gorengann menjual pisang goreng ...

Seorang pedanagan gorengann menjual pisang goreng dan bakwan. Harga pembelian untuk satu pisang goreng Rp1.000,00 dan satu bakwan Rp400,00. Modalnya hanya Rp250.000,00 dan muatan gerobak tidak melebih 400 biji. Jika pisang goreng dijual Rp1.300,00/biji dan bakwan dijual 600,00/biji, keuntungan maksimum yang dapat diperoleh pedagang adalah...

 

  1. Rp102.000,00

  2. Rp96.000,00

  3. Rp95.000,00

  4. Rp92.000,00

     

  5. Rp86.000,00

     

Jawaban:

Misalkan;

 

Pisang Goreng

Bakwan

Modal/muatan gerobak

Harga(Rp)

1.000

400

250.000

Muatan

x

y

400

 


space S e h i n g g a space m o d e l space m a t e m a t i k a n y a space y a i t u colon space  1000 x plus 400 y less or equal than 250.000 space left parenthesis divided by 200 right parenthesis left right arrow 5 x plus 2 y less or equal than 1250 space space space horizontal ellipsis space left parenthesis 1 right parenthesis space  x plus y less or equal than 400 space space space horizontal ellipsis space left parenthesis 2 right parenthesis space  x greater or equal than 0 comma d a n space y greater or equal than 0 space space  C a r i space t i t i k space p o j o k n y a comma space y a i t u colon  5 x plus 2 y less or equal than 1250 space left right arrow left parenthesis 250 comma 0 right parenthesis d a n space left parenthesis horizontal strike 0 comma 625 end strike right parenthesis space x plus y less or equal than 400 left right arrow left parenthesis horizontal strike 400 comma 0 end strike right parenthesis d a n space left parenthesis 0 comma 400 right parenthesis  S e p e r t i space p a d a space g a m b a r

S e l a n j u t n y a space c a r i space t i t i k space p o t o n g space d a r i space k e d u a space p e r t i d a k s a m a a n space t e r s e b u t comma space m a k a colon  5 x plus 2 y equals 1250 space open vertical bar x space 1 close vertical bar space space 5 x plus 2 y equals 1250  x plus y equals space 400 space space space space space space space open vertical bar x space 2 close vertical bar space 2 x plus 2 y equals 800 minus  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 3 x equals 450 left right arrow x equals 150  S u b s t i t u s i k a n space n i l a i space x comma space k e space p e r s a m a a n space x plus y equals 400 comma space m a k a space d i p e r o l e h colon space  150 plus y equals 400 left right arrow y equals 250 space  S e h i n g g a space t i t i k space p o t o n g n y a space y a i t u colon space left parenthesis x comma y right parenthesis space equals left parenthesis 150 comma 250 right parenthesis. space space  K e u n t u n g a n space p i s a n g space g o r e n g space R p 300 divided by b i j i space d a n space b a k w a n space R p 200 divided by b i j i comma space s e h i n g g a colon space  f left parenthesis x comma y right parenthesis equals 300 x plus 200 y  space f left parenthesis 250 comma 0 right parenthesis equals 300 left parenthesis 250 right parenthesis plus 0 equals 75.000  space f left parenthesis 0 comma 400 right parenthesis equals 0 plus 200 left parenthesis 400 right parenthesis equals 80.000 space  f left parenthesis 150 comma 300 right parenthesis equals 300 left parenthesis 150 right parenthesis plus 200 left parenthesis 250 right parenthesis equals 95.000 space left parenthesis M a k s i m u m right parenthesis space  J a d i comma space k e u n t u n g a n space m a k s i m u m space y a n g space d i p e r o l e h space p e d a g a n g space t e r s e b u t space a d a l a h space R p 95.000 comma 00

 

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