(b) The number of machine hours required for each unit of the respective products is shown in the following table. Suppose that the unit costs for producing products 1, 2, and 3 are RM 25, RM 10, and RM 15, respectively, and that the prices required (in RM) in order to be able to sell x_1, x_2, and x_3 units are (35 + 100x^-1/3_1), (15 + 40x^-1/4_2), and (20 + 50x^-1/2_3), respectively. (i) Formulate a nonlinear programming model for the problem of determining how many units of each product the firm should produce to maximize the profit. (ii) Verify that this problem is a convex programming problem.

## Expert Answer

As there is no limit, it can go as much as it can, so there needs to be additional constrain for the same.

x1 | x2 | x3 | |

42443371.29 | 53687091 | 2122169 | |

Mc Type | Prod 1 | Prod 2 | Prod 3 |

Milling | 9 | 3 | 5 |

Lathe | 5 | 4 | 0 |

Grinder | 3 | 0 | 2 |

Cost | 25 | 10 | 15 |

Price | 34917.15366 | 3438.95 | 72858.32 |

Profit | 111164.4278 | ||

Maximization |

This is a sample not the optimal solution. Optimal solution is infinity.