Question

A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below: Type of toys Machines I II III A 12 18 6 B 6 0 9 Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

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Solution

Let the number of toys of type A be

Items | Number | Machine I | Machine II | Machine III | Profit |

Type A | | | | | Rs. |

Type B | | | | | Rs. |

Max available time | | | |

The equation for machine A is given as,

The equation for machine B is given as,

The equation for machine C is given as.

We need to maximize the cost so we can use function which

All constraints are given as,

| | |

| | |

| | 60 |

| 40 | |

Plot the graph using equations of constraint.

Substitute the value of

Corner points | Value of Z |

| |

| |

| |

| |

Thus, the cost will be maximum if the number of type A toys are

1

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