A price-taking firm produces a single output using two inputs, x1 and x2, according to the production function, f(x1, x2) = 3x1 + 6x2. (30 points)

(a) Write the equation of the y-unit isoquant. Graph the isoquant, placing x2 on the vertical axis and x1 on the horizontal axis. Label any interesting points (intercepts, kinks, etc.), as well as the slope of the isoquant. (6 points)

(b) Suppose that the firm would like to produce y units of output, the price of input 1 is w1 = 2 and the price of input 2 is w2 = 3. Solve for the cost-minimizing input bundle. (6 points)

(c) Continuing with part (b): Solve for the firm's cost function, marginal cost function, and average total cost function. (6 points) For the remainder of the question, consider the firm's short-run cost minimization problem. Suppose that in the short run, the level of x1 is fixed at 3.

(d) Solve for the cost-minimizing choice of x2 if the firm wants to produce 2 units of output. How would your answer change if the firm wanted to produce 4 units of output? (6 points)

(e) Solve for the cost-minimizing choice of x2 if the firm wants to produce y units of output. (6 points)