Suppose the following is the mathematical model: Max 14x s.t. ax 65 X0 where a is the number of hours required for each unit produced. With a = 5, the optimal solution is x = 13.00. If we have a stochastic model with a = 3, a = 4, a = 5, or a = 6 as the possible values for the number of hours required per unit, what is the optimal value for x? Round your answers for the optimal solution to two decimal places. Round the answers for profit to the nearest dollar. and profit = $ If a = 3, x = If a = 4, x = and profit = $ If a = 5, x = and profit = $ If a = 6, x = and profit = $ What problems does this stochastic model cause? The problem with this stochastic model is with certainty. and therefore the values of are not known 2 4. Let random variables X and X2 be the returns of two assets where X ~ N(, ) and X2N(, 02) with the common ER and 0 < 0 < 02 1 (a) Show mathematically that none of X nor X2 first-order stochastically dominates another. (b) Show that X second-order stochastically dominates X2. Consider the following true regression model: Y = 16.2+0.75Xi + i, i = 1,...,N- If Y = -3.2 and X = -20: the residual for observation 5 equals -4.4 the residual for observation 5 equals -5.5 the stochastic error term for observation 5 equals -4.4 the stochastic error term for observation 5 equals -5.5 the residual for observation 5 equals 7.7