## EXPERT ANSWER

1) Solution: optimal solution : 10,560

Working:

Standard Model (x) | Deluxe Model (y) | Maximum Total Profits | ||||

No of Bags | 300 | 420 | 10,560 | |||

Profit ($) / Bag | 10 | 18 | ||||

Constraints | Total Hours of Prod. Used | Total Hours of Prod. Available | Slack Time | |||

Cutting and Dyeing | 0.7 | 1 | 630 | ≤ | 630 | 0 |

Sewing | 0.5 | 0.833 | 500 | ≤ | 600 | 100 |

Finishing | 1 | 0.667 | 580 | ≤ | 708 | 128 |

Inspection and Packaging | 0.1 | 0.25 | 135 | ≤ | 135 | 0 |

Thus the optimal solution will be x = 300, y = 420 and the total profit contribution equals 10560 (= 10(300)+18(420) = 10560)

2) Solution: Optimal solution : 14,160

Working:

Standard Model (x) | Deluxe Model (y) | Maximum Total Profits | ||||

No of Bags | 708 | 0 | 14,160 | |||

Profit ($) / Bag | 20 | 9 | ||||

Constraints | Total Hours of Prod. Used | Total Hours of Prod. Available | Slack Time | |||

Cutting and Dyeing | 0.7 | 1 | 495.6 | ≤ | 630 | 134.4 |

Sewing | 0.5 | 0.833 | 354 | ≤ | 600 | 246 |

Finishing | 1 | 0.667 | 708 | ≤ | 708 | 0 |

Inspection and Packaging | 0.1 | 0.25 | 70.8 | ≤ | 135 | 64.2 |

3) Solution: Optimal solution : 7,668

Working:

Standard Model (x) | Deluxe Model (y) | Maximum Total Profits | ||||

No of Bags | 540 | 252 | 7,668 | |||

Profit ($) / Bag | 10 | 9 | ||||

Constraints | Total Hours of Prod. Used | Total Hours of Prod. Available | Slack Time | |||

Cutting and Dyeing | 0.7 | 1 | 630 | ≤ | 630 | 0 |

Sewing | 0.5 | 0.833 | 480 | ≤ | 750 | 270 |

Finishing | 1 | 0.667 | 708 | ≤ | 708 | 0 |

Inspection and Packaging | 0.1 | 0.25 | 117 | ≤ | 135 | 18 |