1. The capacity of the hold in a cargo ship is 15,000 cubic meters. There are three different cargos for shipping x, y, and z. There is an infinite amount of each cargo available. The cargoes have the following details:

 

Cargo	Weight per unit kilograms	Volume per unit Cubic meters	Loading time Per unit hours	Profit per unit €
x	4	25	1	6
y	1	15	2	8
z	2	10	1	5

To ensure the ship is stable the cargo must weigh at least 2,000 kilograms. The ship must be loaded in 20 days. Three dockers work for 10 hours a day each.

Formulate a linear program to find the optimum cargo to ship.