Consider the following mathematical model. Apply graphical solution to find the optimal values of decision variables and calculate the value of the objective function. Assume that only integer values are acceptable for our decision variables. Apply graphical solution to find the optimal values of decision variables and calculate the value of the objective function. Which method is better than the other? Why? Note: without showing the normal vector and isoprofit lines. Your solution is not acceptable. Maximize 3x1 + Xlz Subject to: 2x1 + tixz = 6 Ix < 1.5 lxz = 3.5 X1, Xz2 ≥ 0
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Plot the constraints: - 2x1 + x2 = 6 (this is a straight line passing through points (0,3) and (3,0)) - x1 < 1.5 (this is a vertical line passing through x1 = 1.5) - x2 = 3.5 (this is a horizontal line passing through x2 = 3.5) Show more…
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Consider following mathematical model - Apply graphical solution and find optimal values of decision variables and calculate the value of objective function - Assume only integer values are acceptable for our decision variables, Apply graphical solution and find optimal values of decision variables and calculate the value of objective function. - Which method is better than the other? Why? Note: without showing Normal vector and Isoprofit lines, your solution is not acceptable. Max -x1 + 2x2 Subject to x1 + 3x2 ≥ 3 x1 ≤ 3.5 x2 ≤ 3.5 x1 , x2 ≥ 0
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Consider the two-dimensional linear optimization problem minimize x1 + x2 subject to x1 + x2 ≤ 4 x1 - x2 ≥ 5 x1 ≥ 0 x2 ≥ 0 (a) Draw the feasible region. (b) Is the feasible region bounded, unbounded, or empty? (c) Draw the objective vector and a few level sets of the objective function. (d) Is the objective function bounded or unbounded above over the feasible solution? (e) Is the objective function bounded or unbounded below over the feasible solution? (f) Does the linear optimization problem admit an optimal solution? If so, is this optimal solution unique or are there many optimal solutions? Mark the position of the optimal solution(s) on your drawing. (g) Mark the location of all basic solutions with crosses (%). (h) Compute the coordinates of each basic solution. (i) In your list of basic solutions, indicate which basic solutions are feasible.
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