(30 points) Develop dynamic programming based solution (using a spreadsheet or MATLAB or Python) that solves a 3-class dynamic capacity allocation problem under the following assumptions: at most one booking request takes place in a period and the probability that this arrival is of class is given in the below table along with respective class fares: Class(i) 1 Pi 800 TL 400 TL 150 TL li 0.10 0.15 0.50 2 3 (a) Write the optimality equation vt(x) with t periods to go and x seats remaining and find the expected optimal revenue starting with 200 periods to go and all 100 seats available. (b) Find the expected marginal value of a seat with 10 seats remaining with 50, 40, 30, 20 and 10 periods remaining. (c) Report the protection levels for classes 1 and 2 with 100, 50, and 10 periods remaining. (d) Find the expected optimal revenue with 200 periods remaining if the arrival probability of class 1 customers becomes q = 0.15,0.20, 0.25, while q2 and 43 remain unchanged. Do you accept class 3 customers with 200 periods remaining under these assumptions