The following figure shows a linear programming problem where the shaded region represents the polytope of feasible solutions, the colored lines represent constraint functions, and the black lines represent the contours of the objective function. Darker lines of the objective function contour represent larger values. It also shows five different points, all of which lie within the polytope. The linear program attempts to find the maximum value. Which point corresponds to a solution of the linear program? A) 2 (B) 5 D E 20 2 ...
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- Give 2 examples of the optimization problem and identify the following for each problem: Objective Function Design Variable Constraint8. Which of the following statements about linear programming is FALSE? Select one: a. If the change of the objective coefficient is out of the range of optimality, the optimal solution in terms of decision variables will usually change. b. A redundant constraint is also a non-binding constraint. c. In sensitivity analysis of LP problem, if the resource has been used up, the shadow price would be non-zero. d. A difference between minimization and maximization problems is that minimization problems often have unbounded regions. e. If the RHS of a constraint changes in a profit maximization problem, the iso-profit line will change as well.Solve the following exercise using jupyter notebook for Python, to find the objective function, variables, constraint matrix and print the graph with the optimal solution. Use linear programming methods to solve this problem. Represent the constraints and the objective function mathematically in code. Use Python and the SciPy and Matplotlib libraries to solve the problem and visualize the optimal solution on a graph. Clearly state the optimal solution and any assumptions made while solving the problem. A farm specializes in the production of a special cattle feed, which is a mixture of corn and soybeans. The nutritional composition of these ingredients and their costs are as follows: - Corn contains 0.09 g of protein and 0.02 g of fiber per gram, with a cost of.$0.30 per gram.- Soybeans contain 0.60 g of protein and 0.06 g of fiber per gram, at a cost of $0.90 per gram.0.90 per gram. The dietary needs of the specialty food require a minimum of 30% protein and a maximum of 5% fiber.…
- If the optimal solution of a linear programming problem with two constraints is x=5, y=0, s1=3 and s2=0 , then the basic variables are ____.Dynamic Programming Problem Solve the figure below using the backward recursive equation defining its stages in order to find the optimal solution.6. Consider a modification to the rod-cutting problem in which, in addition to a value pi for each rod, there is handling cost ci that is one and a half times the length of the rod cut plus a flat fee of 3 (i.e., the handling cost to cut a rod of length 5 is 7.5+3 =10). The revenue generated is the sum of the value of the pieces cut minus the sum of handling costs of the cuts. Provide a dynamic programming approach to solve this problem given an initial rod of length n with potential cut lengths of 1, 2, 5, and 7 [Adapted from ITA, pg. 370, 15.1-3] length of cut (i) 1 2 5 7 value (pi) 5 7 30 45 handling cost (ci) 4.5 6 10.5 13.5
- (a) Model this problem as an Integer Program. (b) Ignoring any integer constraints, derive the dual of the IP you found in part (a). Hint: rememberthat a binary constraint decomposes into ≥ 0, ≤ 1, and Integer.Consider the following linear programming problem: Min A + 2B s.t. A + 4B ≤ 21 2A + B ≥ 7 3A + 1.5B ≤ 21 -2A + 6B ≥ 0 A, B ≥ 0 Determine the amount of slack or surplus for each constraint. If required, round your answers to one decimal place. (1) A + 4B ≤ 21 Slack or surplus (2) 2A + B ≥ 7 Slack or surplus (3) 3A + 1.5B ≤ 21 Slack or surplus (4) -2A + 6B ≥ 0 Slack or surplusA circus is planning a tower act in which individuals stand on top of one another's shoulders. Each individual must be both shorter and lighter than the person below him or her for practical and aesthetic reasons. Write a way to determine the maximum feasible number of people in such a tower given the heights and weights of each individual in the circus.
- This problem exercises the basic concepts of game playing, using tic-tac-toe (noughtsand crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3 = 1 and −1 to any position with O3 = 1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval (s) = 3X2(s)+X1(s)−(3O2(s)+O1(s))."Mark on your tree the evaluations of all the positions at depth 2."Consider the version of the dining-philosophers problem in which the chopsticks are placed at the center of the table and any four of them can be used by a philosopher. In other words, a philosopher needs four chopsticks to eat. Assume that requests for chopsticks are made one at a time. Assuming that there are m=4k chopsticks and n=6k philosophers around the table, (i) How many maximum philosophers can eat simultaneously? (ii) Describe a simple rule for determining whether a particular request can be satisfied without causing deadlock given the current allocation of chopsticks to philosophers. (Hint: Use rules similar to the Banker’s algorithm.)Can someone make a code that minimizes 4 different functions with different equations, and maximizes 4 different with equations functions under 10 types of constraints with equations? In matlab code I need to adapt it to my code please? and plot 3D pareto front Regards