5. (12 points) Consider a firm that employs capital k and labour & in production. The production function is f (k, I) = 2/1/311/2. The price of output is p = 1. a) (3 points) Does the technology exhibit constant, decreasing, or increasing returns to scale? b) (4 points) Find the marginal product of each factor and the marginal technical rate of substitution. Determine if the technology has diminishing marginal product in either factor. c) (5 points) Suppose in the short run, capital is fixed at k = 27. What extra information would you need to determine the exact amountt of labour to be employed in order to maximize short-run profits. Provide a suitable number yourself. and find how much labour is employed. Illustrate your answer with a graph