Please answer throughly (and include graph in (b) so that I can completely understand.

2. (a) Clearly state and explain the condition for cost-minimizing use of labor and capital in a production

process, where labor and capital are variable inputs.

(b) Graphically illustrate (manually drawn graph) and explain why the stated condition in (a) is true.

(c) Suppose you manage a firm with the production function Q = F(K, L) = 4K + 8L, and you are able to hire labor at $60 per hour and your rental rate on capital is $20 per hour. Show your steps and calculations to determine the cost-minimizing capital (K) and labor (L) mix to produce 32 units of output (Q).

(d) Provide a graphical illustration (manually drawn graph) to justify your answer in (c).