Suppose that you want to a start a coffee shop business and assume two production inputs (labor and capital) are perfect substitutes. A coffee machine can produce the output of three workers at a given time, and your goal is to sell 100 units of coffee each week. 

a) What is your combination of inputs to maximize profit if the price of the coffee machine is $750 per week and the weekly salary of each worker is $300.

b) What is your combination of inputs to maximize profit if the price of the coffee machine is $750 per week and the weekly salary of each worker is $200.

c) What is the elasticity of labor demand as the wage falls from $300 to $200?

d) With capital on the Y-axis and labor on the X-axis, illustrate two isocost lines that represent the two conditions given in parts a) and b). You can draw both isocost lines on the same graph. As always, clearly label your graphs and provide some context.