KINDLY ANSWER EVERYTHING. SHOW COMPLETE SOLUTION.

You are scheduled to take the final exams in 4 major courses this term - OR 2, ergonomics, Production Systems and Finance. It is one week before the exams and you estimate that you can only spare 50 hours for studying. Based on your track record in passing courses, you estimated that the probability of passing a course is directly proportional to the amount of study time you spend on the course. You also know that you have to spend sufficient study time in blocks of 5 hours each up to a maximum of 20 hours per course. You are not considering the alternative of not studying for any course because that would mean failure. Below are the estimates of the probability of passing a course as a function of study time.

	EXPECTED PROBABILITY OF PASSING/STUDY TIME
SUBJECT	5 hours	10 hours	15 hours	20 hours
OR 2	0.10	0.22	0.47	0.49
Production Systems	0.25	0.40	0.45	0.53
Ergonomics	0.35	0.48	0.65	0.79
Finance	0.50	0.60	0.75	0.85

Solve the problem using DP. Start with Finance as Stage 4. Note: Since probability is given the recursive equation of the previous stage is multiplicative, not additive.

a) Write the recursive equation for Stage 4. _______

b) What is the minimum state at Stage 4? _______

c) Write the recursive equation of Stage 3. _______

d) What is the minimum state of Stage 3? _______

e) If the state is 20 in Stage 3, what is the optimal probability of passing? Answer in 3 decimal places. _______.

What is the optimal value of X3 in this stage? _______

f) At Stage 2, what is the optimal probability of passing at State of 50? Answer in 4 decimal places. _______

What is the optimal value of X2 in this stage?

g) Fill in the correct values at optimal solution.

STUDY SCHEDULE	NUMBER OF HOURS
OR 2	-------
Production Systems	-------
Ergonomics	-------
Finance	-------
Probability of Passing (Answer in SEVEN decimal places)	-------

h) What is the second best solution? Fill in the blanks below.

STUDY SCHEDULE	NUMBER OF HOURS
OR 2	-------
Production Systems	-------
Ergonomics	-------
Finance	-------
Probability of Passing (Answer in FOUR decimal places)	-------

i) If you only have 40 hours of available study hours, what is the optimal policy? Fill in the blanks below.

STUDY SCHEDULE	NUMBER OF HOURS
OR 2	-------
Production Systems	-------
Ergonomics	-------
Finance	-------
Probability of Passing (Answer in FIVE decimal places)	-------