Commuter airplanes flying transcontinental flights typically carry three types of cargo: passengers, luggage, and airmail. Each of these types of cargo have weight and volume limits. There may also be other restrictions. Here is the formulation for the LP problem:
x = Passenger Weight, y = Luggage Weight, z = Airmail Weight

Max Z=5x + 6y + 4z
s.t
x + y + z < 20000     total weight (Pounds)
x < 14000         Allowed weight of Passengers (Pounds)
y < 11000        Allowed weight of Luggage (Pounds)
z < 8000        Allowed weight of Airmail (Pounds)
2y + 3z - x ¬> 0     Other restriction 1
x + 2z < 12000    Other restriction 2
x-y > 0           Passenger weight have to be grater then Luggage weight
   x,y,z > 0    Non negativity

Air Canada flies two round trips from Toronto to Barbados each day, 358 days per year (the rest of the time, the aircraft is in-service). A retrofitting company is currently offering to install a special cargo bay contraption that will allow the plane to carry an extra 1100 lbs per flight at a price tag of $9 million. Should Air Canada hire the retrofitters to modify the aircraft given that they would like to turn a profit on the investment in under 1-year?