The Railroad Flatcar Problem

Background:

Two railroad flatcars are to be loaded with seven types of packing crates. The crates have the same width and height but varying thickness (t, in cm) and weight (w, in kg). Table 1 gives, for each crate, the thickness, weight, and number available. Each car has 10.2 meters of length available for packing the crates (like slices of toast) and can carry up to 40 metric tons. There is a special constraint on the total number of C5, C,6, and C7 crates because of a subsequent local trucking restriction: The total space (thickness) occupied by these crates must not exceed 302.7 cm. Load the two flatcars so as to minimize the wasted floor space.