Trisha's Fashion Boutique Is Considering a Profit Sharing Arrangement with Her

Trisha's Fashion Boutique is considering a profit sharing arrangement with her employees. Currently, the employees receive an annual bonus. In a "Boom" market, Trisha can sell all the output she produces for $225 per unit. In a "Bust" market, Trisha can sell all the output she produces for $125 per unit. The probability of a "Boom" market is 75% and the probability of a bust market is 25%. Trisha's total cost function (including bonus payments to employees) is: TC(Q) = 75Q + 2.5Q². The marginal cost function is: MC(Q) = 75 + 5Q. The profit sharing plan would pay employees 30% of profits. However, due to greater cost saving initiatives from employees, Trisha's total cost function becomes: TC(Q) = 50Q + 2Q². The relevant marginal cost function becomes: MC(Q) = 50 + 4Q. Which plan offers Trisha the greatest expected profits for herself? Suppose the employees will only approve a profit sharing plan if they are guaranteed their portion of profits will be at least $400. Will the employees approve of the profit sharing program?