The production of a strawberry cultivator is dependent on average temperature during a critical period of growth of the plants just before harvest. The production function of the strawberries is given by:Q=L^0.5(T -0.02T²)where L is the number of employees the producer hires and T is the average temperature (in Celsius degrees, T>0) during the critical period.

A) Draw a diagram showing how production relates to the temperature if L=1. Which temperature will yield the highest profit for the producer?

Assume that there are three possible temperature outcomes, A, B and C that will occur with the probabilities p_A=0.2, p_B=0.5, and p_C=0.3. In A the temperature will be 10 degrees, in B 25 degrees, and in C 40 degree. The wage paid to the employees (w_L) is 10 and the strawberries aresold at a price (P) of20 per unit produced. The producer will have to decide on and hire the number of employees before the critical period of growth, i.e. before he knows what the weather and temperature will be like.

B) How many employees will the producer hire in order to maximize expected profits?

C) Now, the producer, who is risk neutral, puts great faith in a local fortune teller when it comes to making weather forecasts. What is the maximum amount the producer would be willing to pay in advance to this fortune teller for a 100% accurate prophecy regarding which of the weather/temperature conditions A, B or C that will occur?