a) The local cleaner launders white clothes using the production function q = 3B + G, where B is the number of cups of a brand bleach and G is the number of cups of a generic bleach that is half as potent.

a.1) In a graph, draw an isoquant.

a.2) What are the marginal product of B and G? What is the marginal rate of technical substitution?

b) The MTA uses equipment (K), labor (L) and supplies (S) to produce public transportation services according to the production function Q =K^(0.5)L^(0.25)S^(0.5).

b.1) What kind of returns to scale does this production function exhibit?

b.2) What is the marginal product of labor? Does the production function exhibit diminishing marginal returns?

b.3) What is the marginal rate of technical substitution of equipment for labor services? Does it depend on the MTA's usage of supplies?

b.4) Assume that K = 16. In a diagram measuring labor along the horizontal axis and supplies along the vertical axis draw one of the MTA's isoquants.