The following number and type of plumbing fixtures serve an apartment: one bathtub, one water closet, one lavatory, one kitchen sink, and one dishwasher. Assume the horizontal fixture branch serving these fixtures flows into a waste stack. Assume the vent stack extends through the roof and is 14 ft long. Determine the minimum pipe diameter required for:
a. The horizontal fixture branch
b. The waste stack at base of stack
c. The vent stack at top of stack