linear programming help?

Question

what varibales do i need to define and how do i use them to to write a linear program that optimizes revenue with this
constraints:
we have a ship that can carry a maximum weight of 100 tons of cargo and a maximum volume of 60 cubicmeters. we have three materials to be transported, and we may carry any amount of each, up to the maximum available limits given below:
·Material 1 has density 2 tons/cubic meter, maximum available amount 40 cubic meters, and revenue $1,000 per cubic meter.
·Material 2 has density 1 ton/cubic meter, maximum available amount 30 cubic meters, and revenue $1,200 per cubic meter.
·Material 3 has density 3 tons/cubic meter, maximum available amount 20 cubic meters, and revenue $12,000 per cubic meter
could you please explain me the steps, i am getting ready for an exam and need to understand this practice problem. thanks for your explaination in advance.

Answer 1

let :
m1 volume of material 1, m2 of material 2 m3 of material 3

then
constraints

max availability :
0 <= m1 <= 40
0 <= m2 <= 30
0 <= m3 <= 20

max volume on ship
m1 + m2 + m3 <= 60

constraints for weight
2m1 + 1m2 + 3m3 <= 100

you should maximize the revenues i guess so :

maximize P(m1,m2,m3) = 1000m1+ 1200m2 + 12000m3


that is all.