Write a Quantitative Analysis report on the following problems:

A) The owner of a car wash is trying to decide on the number of people to employ based on the following short-run production function:Q = 6L - 0.5L2

Where Q = Number of car washers per hour L = Number of workers

Generate a schedule showing total product, average product, and marginal product, Plot this schedule on a graph.

Suppose the price of basic car wash (no undercoating, no waxing treatment, etc) in his area of business is $5. How many people should he hire if he pays each worker $6/hour?

Suppose he considers hiring students on a part-time base for $4/hour. Do you think he should hire more workers at this lower rate? Explain.

B) You are given the following cost functions:

TC = 100 + 60Q - 3Q2 + .1Q3

TC = 100 +60Q + 3Q2

TC = 100 + 60Q

Compute the average variable cost, average cost, and marginal cost for each function. Plot them on a graph.

In each case, indicate the point at which diminishing returns occur. Also indicate the point of maximum cost efficiency (i.e. the point of minimum average cost). Is this company operating in stage II?

For each function, discuss the relationship between marginal cost and average variable cost and between marginal cost and average cost. Also discuss the relationship between average variable cost and average cost.