A woodworking company handcrafts two types of birdhouses. One is large and the other is small. Both types of houses go through two technicians; first a shaper and then a painter. The large house requires two hours of the shaper's time and one hour of the painter's time. The small house requires one hour of the shaper's time and two hours of the painter's time. The shaper has 104 hours and the painter has 76 hours of time available this month. Profit on the large house is $6 and on the small house is $11. The following inequalities are formed from the information provided:
Let x = large birdhouses and y = small birdhouses.
x ≥ 0, y ≥ 0
2x + y ≤ 104 (shaper)
x + 2y ≤ 76 (painter)
Assuming that all the houses that are produced can be sold, how many of each type of house should the company manufacture per month to obtain the best returns?