A manufacturer produces and sells chilled, ready-to-eat pasta salad in round lots of 50 serving units each. These items have a very limited shelf life; therefore, if items are made but not sold, they have no value. Conversely, if demand exceeds supply during the week (regular production runs are made on Friday of each week for sales the following week), an extra production run can be made. The cost per unit for a regular run is $5 per unit, whereas the cost of an extra production run is $7 per unit. All items are sold for $10 per unit regardless of production cost. Historically, demand has been for 50, 100, or 150 units each week, so the company makes one of those run sizes. In the past, the manager of the department has made 100 units per week for regular production.A: Prepare a payoff table showing profits for each of the lot sizes.B: If probability of demand for 50 units is .40, probability of demand of 100 units is .50, and probability of demand for 150 units is .10, what lot size would you recommend if the goal is to maximize expected profit?