Please answer thoroughly and thank you

Consider the following objective and constraints:

Maximize Z= 0.5x^5 - 6x^4 + 24.5x^3 - 39x^2 + 20x

subject to x<=5; x>=5

1) Using x = 2.5 as the initial trial solution, perform five iterations of the basic simulated annealing algorithm by hand. Whenever random numbers are needed, use the random numbers listed below sequentially from left to right for each row (you may not need to use all of them). Use an initial temperature value equal to the objective function value of the initial solution. To generate neighbors, randomly increment or decrement the value of x by 1 by using random numbers where you decrement if the random number is 0.5 or less; otherwise, you increment (again, continue to use the random numbers below). Make sure a neighbor is feasible

2) Reduce the temperature geometrically by a factor =0.8 and perform 5 more iterations manually

3) Solve the model using the evolutionary solver in Excel and report the solution obtained

4) Find the optimal solution using Excel solver and compare the solution to the one obtained using the evolutionary solver

5) Solve using Tabu Search with a tabu list size of 2 and a neighborhood size of 2. One neighbor is generated by adding 0.5 to the value of x and the second by subtracting 0.5 from the value of x. As in Problem 1, the initial value of x=2.5. Run the algorithm for 5 iterations manually and show your computations.

Show your work, including the use of the random numbers.

Random numbers

.09656, .24712, .07202, .84575, .38144, .48048, .41936, .73391, .57580, .92646, .07118, .57842

.65078, .04294, .48381, .00459, .38824, .91465, .50874, .26644, .96657, .55799, .96341, .46820

.87037, .56349, .58566, .94006, .08954, .41113, .12707, .57831, .44981, .96120, .06807, .62045

.81681, .22232, .00807, .75871

Problem 2 (20 points)

Solve using Tabu Search with a tabu list size of 2 and a neighborhood size of 2. One neighbor is generated by adding 0.5 to the value of x and the second by subtracting 0.5 from the value of x. As in Problem 1, the initial value of x=2.5. Run the algorithm for 5 iterations manually and show your computations.