Q1) Write MATLAB program to evaluate the max/min of a function using the bisection method.

Let f(x)=((x-0.085)*1000)/(x^2) and the interval [0, 0.6] for 11 points

Q2) In probabilistic dynamic problem use Value iteration, or successive approximations method to define the optimal policy using matlab.

Q3) In probabilistic dynamic problem use policy iteration method to define the optimal policy, using matlab.

In Q1 and Q2 Consider the problem

At the beginning of each week, a machine is in one of four conditions (states): excellent (E), good (G), average (A), or bad (B). The weekly revenue earned by a machine in each type of condition is as follows: excellent, $100; good, $80; average, $50; bad, $10. After observing the condition of a machine at the beginning of the week, we have the option of instantaneously replacing it with an excellent machine, which costs $200. The quality of a machine deteriorates over time, as shown in Table 8. For this situation, determine the state space, decision sets, transition probabilities, and expected rewards. TABLE 8 Next Period's States of Machines Present State of Machine Probability That Machine Begins Next Week As Excellent Good Average Bad .7 .3 .7 Excellent Good Average Bad | .4 1.0 until replaced