Among the many customers of railway companies, there are several mining companies that use the network to transport ore from the mines to the factories in order to process it. One of these mining companies uses a CN freight train to transport three types of ore: copper, titanium, and iron. When transporting ore, however, there are a few constraints to be observed. First of all, the freight train cannot transport more than 5,000 tons of gold. Then, due to supply and demand, the amount of copper never twice exceeds the amount of titanium, and more, the amount of titanium never exceeds the amount of iron. Transporting these minerals is a source of profit for CN. Each ton of copper earns $35, each ton of titanium earns $20, and each ton of iron earns $10.

a) You are asked to determine how much of each type of ore the freight train should carry in order to maximize the profit for the railroad company.

b) In the first octant of Cartesian space, illustrate the constraint that the freight train cannot transport more than 5,000 tons of ore.