Please can someone help me with parts e, f, and g? I am struggling because of the fixed element.

2. Consider a firm with production function q=1000lk. Suppose that the monthly rental rate on capital is v=12000 per machine and the monthly wage rate for labor is w=3000 per worker. (a) What is the formula for the marginal rate of technical substitution in this case? (b) How much capital and labor would the firm hire and what would its cost be if it planned to produce: i. q=4,000 units, ii. q=10,000 units, iii. q=20,000 units? (c) What is the firm's long-run cost function C(q) ? Sketch this function in a graph with dollars on the vertical axis and output on the horizontal. (d) What are its long-run average and marginal cost functions, AC(q) and MC(q) ? Sketch these functions in a second graph (below your first graph) with dollars per unit of output on the vertical axis and output on the horizontal axis. Suppose for the rest of the question that the firm's capital stock is fixed at k0=5 machines in the short run. (e) How much labor would the firm hire and what would its total cost be if it produced: i. q=4,000 units, ii. q=10,000 units, iii. q=20,000 units? (f) What are the firm's short-run total, fixed, and variable cost functions, SC(q),FC, and VC(q) ? Sketch the short-run total cost function in the same graph as the long-run cost function. (g) What are its short-run average total, average variable, and marginal cost functions, SAC(q), AVC(q), and SMC(q) ? Sketch these three functions in the same graph as long-run average and marginal costs. (Hint: SAC(q) is U-shaped. At the output, q, where it reaches its minimum, the following equalities hold: SAC(q)=SMC(q)=AC(q).) 2. Consider a firm with production function q=1000lk. Suppose that the monthly rental rate on capital is v=12000 per machine and the monthly wage rate for labor is w=3000 per worker. (a) What is the formula for the marginal rate of technical substitution in this case? (b) How much capital and labor would the firm hire and what would its cost be if it planned to produce: i. q=4,000 units, ii. q=10,000 units, iii. q=20,000 units? (c) What is the firm's long-run cost function C(q) ? Sketch this function in a graph with dollars on the vertical axis and output on the horizontal. (d) What are its long-run average and marginal cost functions, AC(q) and MC(q) ? Sketch these functions in a second graph (below your first graph) with dollars per unit of output on the vertical axis and output on the horizontal axis. Suppose for the rest of the question that the firm's capital stock is fixed at k0=5 machines in the short run. (e) How much labor would the firm hire and what would its total cost be if it produced: i. q=4,000 units, ii. q=10,000 units, iii. q=20,000 units? (f) What are the firm's short-run total, fixed, and variable cost functions, SC(q),FC, and VC(q) ? Sketch the short-run total cost function in the same graph as the long-run cost function. (g) What are its short-run average total, average variable, and marginal cost functions, SAC(q), AVC(q), and SMC(q) ? Sketch these three functions in the same graph as long-run average and marginal costs. (Hint: SAC(q) is U-shaped. At the output, q, where it reaches its minimum, the following equalities hold: SAC(q)=SMC(q)=AC(q).)