Consider a risk-neutral manager who can either work or shirk. If he works, the outcome of the firm will be 100 with probability 0.8 and 30 with probability 0.2. If he shirks the outcome will be 100 with probability 0.3 and 30 with probability 0.7. Assume that working is associated with a cost of 5 to the manager (shirking is not associated with a cost). Also assume that the manager's effort choice (work/shirk) is non-observable to anybody except the manager. Assume that the manager obtains the following pay scheme: If the outcome is 100 he obtains the pay pu and if the outcome is 30 the pay is pu. Hence, his total payoff if he works is 0.8pu + 0.2pL-5 and if he shirks his payoff is 0.3pu + 0.7pL. Assume the board of directors has two goals: i) it wants to induce the manager to work and ii) wants to use a cost effective incentive scheme (i.e., wants to keep the cost of the incentive scheme as low as possible). Also assume that the payments pu and pL must be non-negative. What are the optimal payments pu and pu? Also determine the expected cost of the compensation scheme for the firm. Please provide all calculations and explain your answers