Consider the average reward version of the model in Problem 6.1. a. Show that the model is…

Consider the average reward version of the model in Problem 6.1.

a. Show that the model is recurrent.

b. Find a .Ol-optimal policy using value iteration.

c. Find an optimal policy using policy iteration.

d. Show that the model satisfies one of the hypotheses of Theorem 8.5.3 and conclude that value iteration converges. Determine its rate of convergence with respect to the span seminorm.

e. Find an optimal policy using modified policy iteration.

f. For what values of h is the average optimal policy equal to the optimal policy for the discounted model?

g. Solve the problem using linear programming.

h. Solve a constrained version of the problem, in which the averagc cost of sending catalogs does not exceed $7.50 per period. Investigate the sensitivity of the optimal policy to this cost. Display your results graphically by plotting the optimal policy versus this cost.

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