1) Tracy is a salesperson working for PLUM autonomous drone company. The utility function of Tracy is given by u(w,b,e) =w+ b c(e) where w R is Tracy's weekly wage, b is a bonus payment that is conditional on sales revenue, and c(e) is Tracy's cost of effort where cle) =7 ife if e > 10. Jane is Tracy's boss, who is maximising PLUM's profits which are given by: n(w,b,e) = R(e) w b, where R(e) is the firm's weekly sales revenues and R(e) = 200e Jane cannot observe Tracy's effort (e) directly but observes the sales revenue R(e) and can set the bonus payment b to depend on sales revenues. . Suppose Jane sets Tracy's weekly wage to be $983 and the bonus payment b to be zero. What would be Tracy's effort level (e) and PLUM''s profits? (1 mark) Suppose Jane sets Tracy's weekly wage to be $83 and the bonus payment b to be $805 conditional on reaching a sales target of R(e) = 8000 (i.e., b=0 if sales revenues are lower than $8,000). What would be Tracy's effort level (e) and PLUM's profits? (1 mark) Suppose Jane sets Tracy's weekly wage to be $773 and the bonus payment to be 20% of sales revenues (i.e. b = 0.2 X R(e)). What would be Tracy's effort level (e) and PLUM's profits? (1 mark) . What is the optimal wage (w R) and the bonus payment b that maximises PLUM''s profits? (2 marks) Briefly discuss the potential challenges with implementing an employment contract as in d) in a real-world setting. (2 marks)