It would be great and I would sincerely appreciate if this question can be answered with detailed explanation. Thank you!

Consider a firm that uses both capital (K) and labour (L) to produce a final product (Q) that it sells at the market price $5. The firm buys Labour at a cost of $4 per unit and capital at a cost of $10 per unit. The firm is a price-taker for all prices with the following production function: Q=4K1/2L1/2 This production function implies the following: MPK=2K1/2L1/2MPL=2L1/2K1/2 Suppose also that the firm currently has 16 units of capital (K=16) in the Short-Run. For Q1 - Q6, assume that we are operating in the Short-Run: 1. Given the above production function, write down an expression for Labour employed as a function of the quantity produced (i.e. L=f(Q)). [1 point] 2. Use the MPL and the wage rate to write down an expression for the Firm's Marginal Cost per unit of output (Q) produced as a function of Q. [3 points] 3. Show that the firm's profit-maximizing quantity (Q) is equal to 160 in the short-run. [1 point] 4. What are the firm's variable costs (VC) and fixed costs (FC) at Q ? [2 points] 5. What are this firm's short-run profits in this example? [ 1 point] 6. What would be the firm's Short-Run profits if it chooses to shut down? Should the firm keep producing in the short-run? How do you know? [2 points] Consider a firm that uses both capital (K) and labour (L) to produce a final product (Q) that it sells at the market price $5. The firm buys Labour at a cost of $4 per unit and capital at a cost of $10 per unit. The firm is a price-taker for all prices with the following production function: Q=4K1/2L1/2 This production function implies the following: MPK=2K1/2L1/2MPL=2L1/2K1/2 Suppose also that the firm currently has 16 units of capital (K=16) in the Short-Run. For Q1 - Q6, assume that we are operating in the Short-Run: 1. Given the above production function, write down an expression for Labour employed as a function of the quantity produced (i.e. L=f(Q)). [1 point] 2. Use the MPL and the wage rate to write down an expression for the Firm's Marginal Cost per unit of output (Q) produced as a function of Q. [3 points] 3. Show that the firm's profit-maximizing quantity (Q) is equal to 160 in the short-run. [1 point] 4. What are the firm's variable costs (VC) and fixed costs (FC) at Q ? [2 points] 5. What are this firm's short-run profits in this example? [ 1 point] 6. What would be the firm's Short-Run profits if it chooses to shut down? Should the firm keep producing in the short-run? How do you know? [2 points]