Draw and dimension the load and reaction diagram, the shear diagram, and the bending momen...

Draw and dimension the load and reaction diagram, the shear diagram, and the bending moment diagram for the beams shown in the following figures:

The rectangular coverless box of Fig. 1 has a width x, length ky (where k is a known constant), and height y. Find the relationship between x and y if the area of the plate material is to be a minimum for a given volume for the box level full.

Figure 1