Dynamic programming

it’s dynamic programming questions

All answers needs to be done Manually like no excel or python

You can write down the answers on Word or google doc

You have to solve problem 1

And choose between problem 2 A or Problem b to slove it

ISE 3102 – Exam 2 part b
Problem 1-15 pts
A new airline is going to operate out of Philadelphia and it is allowed to schedule only 6 flights per day.
The destinations can only be New York, Los Angeles or Miami. Each of those flights gives a different
profit per flight as shown in the table below. They wish to maximize their profit and want to know the
best way to schedule.
(15 pts) Write the recursion equation describing this.
Destination
NY
LA
Miami
1
80
100
90
Profit per Flight($)
# planes
2
3
150
210
195
275
180
265
4
250
325
310
5
270
300
350
6
280
250
320
Problem 2 (do EITHER problem A or B) 15 pts
Problem A
10 pts) In class we played a game involving a spinner in which you won a certain amount based on
where the spinner landed. You were allowed to spin up to m times (and you selected m prior to starting
the game). Now, you are playing a game of chance exactly four times. The chance of winning a bet is
40%. If you have d dollars, in each bet you can bet 0,1,2,…d dollars. If you win, you receive your bet back
and an amount equal to your bet. (i.e. If you bet $2 and win, you now have $4, if you lose you have $0).
You have only $2 and your goal is to find a strategy that will maximize your chance of ending up with at
least $6 (you must quit either when you are broke or have $6 if either is before your 4th turn). Solve
using dynamic programming and make sure you define your stages, states, variables, etc…
Problem B
Beer pong is your specialty sport. On your turn you can have up to two serves. When you serve the ball
it can land in regulation or not. If the ball lands in regulation on the first serve there is a chance for a
second serve. If the ball does not land in regulation on the first serve, the point is over and it is your
opponent’s turn. You have only two types of signature serves: the backspin (B) and the forehand (F).
The probability that B lands in regulation is 65% and the probability that F lands in regulation is 90%,
since the backspin requires much more skill. If the backspin lands in regulation, then you have a
probability of 80% of winning the point. If the forehand lands in regulation, you have a 65% chance of
winning the point. The payoff is 1 if you win, and 0 if you lose.
Each point has only a maximum of 2 serves. Your job is to determine a policy for how to serve the (at
most) 2 serves for each point. Solve using dynamic programming and make sure you define your
stages, states, variables, etc…