Graph

Maximize: z = 3x + 5y Subject to

x +4y ≤ 24 3x + y ≤ 21

x + y ≤ 9 x ≥ 0 , y ≥0

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#### Solution

Inequation | Point on x-axis | Point on y-axis | Feasible Region |

x +4y ≤ 24 | (24,0) | (0,6) | Origin side |

3x +y ≤ 21 | (7,0) | (0,21) | Origin side |

x + y ≤9 | (9,0) | (0,9) | Origin side |

From the figure common feasible region is ABCDEA

E is the point of intersection of x + y = 9 and x + 4y =24

Solving them we get E(4,5)

D is the point of intersection of x + y = 9 and 3x +y = 21

Solving them we get D(6,3)

End Point | Value of z = 3x +5y |

A(0,6) | 0 +30= 30 |

B(0,0) | 0 + 0 = 0 |

C(7,0) | 21 + 0 = 21 |

D(6,3) | 18 +1 5 = 33 |

E(4,5) | 12 +25 = 37 |

∴ z is maximum 37 at the point (4, 5)

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