A firm with one worker wants to establish a wage Y=a+bQ where Q is worker output. The firm's output is given by Q=3E. Here, E is worker effort and a and b are numbers to be chosen by the firm. The worker maximizes utility which is given by

U=wage-0.5E^2 or U=(a+bQ)-0.5E^2. Where the latter term reflects the cost of the effort to the worker.

The product sells for $11 per unit. Each unit of output requires $1 in material costs.

A) Derive the worker's optimal effort E* for a given a and b. Show your work and prove that the worker has maximized their utility

B)Continuing the above question, what are the best new revenues per unit produced?

C)Assume that the worker's utility must be at least zero for him or her to accept the job. Calculate the profit maximizing values of a and b, and the optimal effort E*, output Q and profit (pi) that results.