Suppose the following is the mathematical model: Max 11x s.t. ax 65 X 0 where a is the number of hours required for each unit produced. With a = 4, the optimal solution is x = 16.25. If we have a stochastic model with a = 2, a = 3, a = 4, or a = 5 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. If a = 2, x = and profit = $ If a = 3, x = and profit = $ If a = 4, x = and profit = $ If a = 5, x = and profit = $ What problems does this stochastic model cause? The problem with this stochastic model is a is not known with certainty certainty. and therefore the values of x and profit are not known with Max has a lot of data from stochastic process: xt = 0.98xt-1 t - 0.1t-1 where t ~ N (0,0) are Gaussian white noise. He tests for a unit root and mistakenly decides that the stochastic process is integrated of order 1. He then differences the data to obtain t = = Axt A) Write out the ARMA model for yt [2 points] B) If you were to fit an ARMA model to yt, what would the order of the AR and MA components be? [2 points] C) Is Xt causal? [1 point] D) Is the ARMA model for yt stationary? [1 point] E) Is the ARMA model for yt invertible? [2 points] F) Knowing the ARMA model for yt = Axt, would you expect the ACF for Yt, to cut off abruptly after 2 lags? Explain why. [1 point] G) Knowing the ARMA model for yt = Axt, would you expect the PACF for Yt, to cut off abruptly after 1 lag? Explain why. [1 point] > Problem 1-09 (Algorithmic) Suppose the following is the mathematical model: Max 15x s.t. ax 20 X0 where a is the number of hours required for each unit produced. With a 4, the optimal solution is x = 5.00. If we have a stochastic model with a = 2, a = 3, a = 4, or a 5 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. If a = 2, x = and profit = $ If a = 3, x = and profit = $ If a = 4, x = and profit = $ If a = 5, x = and profit = $ What problems does this stochastic model cause? The problem with this stochastic model is and therefore the values of x and profit are not known with certainty.