Question

Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) 2) 3) Every basic solution in the assignment problem is necessarily degenerate. The assignment problem cannot be solved using the transportation technique. If the gradient vector of a function at a given point is zero, the point can only be a maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum 5) The Golden Section Search method gives better results than the Fibanocci Search method. 6) If we use the Fibanocci Search method to find the value of x that minimize the function f(x)-x +4cos(x) in the interval [1, 2] and we want to locate the value ofx to within a range of 0.2, then 3 iterations are needed to obtain the solution. The Newton Method gives less accurate results than the Secant Method. 7) An assignment problem can be formulated as a linear programming problem, it is solved by special method known as the Hungarian method. 8) b) (3 Marks) Write a MATLAB m-file to solve the following problem, maximize Z-34-2x, + 5x3-4x, subject to X1-221 X, 20, Х, 20, Х, 20, Х,20.

Answer 1

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          Please find the answer to Q1-4 attached as under. Please give a thumbs up rating if you find the answer useful! Have a rocking day ahead!

1. True, because every feasible solution of the assignment problem having a square payoff matrix of order n should have 2n-1 assignments. Also, due to the structure of the problem, any solution can have more than n assignments. Thus, every solution is inherently degenerate.

2. False, the problem can be solved using transportation techniques, due to which the statement in problem 1 is true.

3. True, because that is the property of the maxima/minima.

4. False, because the region between the two minima may have a flat gradient at all places.

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