We operate a cargo plane that can hold up to 30,000 pounds of cargo
occupying up to 20,000 cubic feet. We have contracted to transport
the following items:

Item |
Weight |
Volume |
Number |
Cost if not carried |

1 | 4,000 | 1,000 | 3 | $ 800.00 |

2 | 800 | 1,200 | 10 | $ 150.00 |

3 | 2,000 | 2,200 | 4 | $ 300.00 |

4 | 1,500 | 500 | 5 | $ 500.00 |

For example, we have contracted to take 10 items of type 2, each of which weighs 800 pounds and takes up 1200 cubic feet of space. The "cost" column refers to the cost of subcontracting shipment of one item to another carrier.

For each pound we carry, the cost of flying the plane increases by 5 cents.

Which items should we put in the plane, and which should we ship via the other carrier, in order to have the lowest total cost?