2. The owner of Neumann's Pool service believes that the short-run relationship between the number of pools cleaned (Q - ouotput) and labor input (L) is described by the following production function: Q = 2 + 7.5 L - .5 L2 Q is the number of pools cleaned/day. L is the number of people employed/day The price the firm receives is $30 (PX = $30) for each pool cleaned and the daily wage for labor (L) is $ 15/day (W = $15). All other costs are assumed trivial (ie. 0). a. How many units of labor (L) should be employed to maximize profit? b. What is the profit maximizing output level Q? c. What will be the firms profit at this level of output? d. Suppose a minimum wage is passed by Congress which raises the W to $18/hour. What will happen to the profit maximizing quantity of labor hired and the profit maximizing output level and profits? e. Suppose the inflation increases the price of pool maintenance and price of labor both increase by 20%. How will that impact the optimal number of units of labor hired and production Q change? f. Suppose there is inflation which increases the price of pools by 50% to $45/pool but the daily price of labor only increases by 33.33% to $20/day. How would this impact the optimal number of labor units employed, production Q, and profits