A shipping company has the capacity to move 100 tons/day by air. The company charges $250/ton for air freight. Besides the weight constraint, the company can only move 50,000 ft3 or cargo per day because of limited volume of aircraft storage compartments. The following amounts of cargo are available for shipping each day:
Day Cargo Weight (tons) Volume (ft3/ton)
1 30 550
2 40 800
3 50 400

a) Determine how many tons of each cargo should be shipped by air each day in order to maximize revenue.

The company has the capability to reconfigure some of its older planes to
increase the size of the cargo areas. The modifications would cost $200,000 per plane and would add 2,000 ft3 per plane. The weight limits would stay the same.

b) Assuming that the planes fly 250 days per year and that the remaining lifetime of the older planes is around five years, would it be worthwhile to make the modifications?

c) To how many planes would it be worthwhile?

Please show all work.