Suppose that a clothing firm has orders to produce 1000 hoodies. The price of capital is $1000, the price of labour is $25, and their production function is given as follows:

Q = f( K, L) = 3K1/3L 2/3

a. Calculate the marginal rate of technical substitution (MRTS).

b. Determine the capital to labour ratio.

c. What is the optimal quantity of labour and capital to employ if the firm produces 1000 hoodies?

d. What is the total cost of producing 1000 hoodies?

e. Suppose that the selling price of each hoodie is $80, what is the firm's profit or loss?

f. Draw an isoquant and an isocost curve on a diagram showing the optimal quantity of labor and capital at 1000 hoodies with capital on the y axis and labour on the x-axis. Show the intercepts and accurately label the graph