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Title: What combination of x and y will yield the optimum for this problem?Minimize $3x + $15y, subject to ... Post by: Apatix on Jul 14, 2017 What combination of x and y will yield the optimum for this problem?
Minimize $3x + $15y, subject to (1) 2x + 4y ≤ 12 and (2) 5x + 2y ≤ 10 and (3) x, y ≥ 0. A) x = 2, y = 0 B) x = 0, y = 0 C) x = 0, y = 3 D) x = 0, y = 5 E) x = 1, y = 5 Title: Re: What combination of x and y will yield the optimum for this problem?Minimize $3x + $15y, subject ... Post by: Almeyric on Jul 14, 2017 Content hidden
Title: Re: What combination of x and y will yield the optimum for this problem?Minimize $3x + $15y, subject ... Post by: phil13 on Mar 7, 2020 thank you
Title: BFSF: What combination of x and y will yield the optimum for this problem?Minimize $3x + $15y, subject to ... Post by: Lim Rachael on Sep 18, 2023 Help! The answer is missing an explanation...
Title: Re: What combination of x and y will yield the optimum for this problem?Minimize $3x + $15y, subject ... Post by: Almeyric on Sep 18, 2023 Since it's been a while since I answered, I have another question with its solution taken from my notes.
(https://biology-forums.com/gallery/qpics/6_18_09_23_11_21_24.png) Solution We know that the optimal solution occurs at corner points of the feasible region. Since this feasible region is bounded by ">=" constraints, we know that the 2 constraints will intersect with each other and with the x and y axes. We evaluate the objective function of each of these points (the intersection of the two constraints, the intersection of the constraints with the axes). We can graph the constraints to determine the coordinates of these points: (https://biology-forums.com/gallery/qpics/6_18_09_23_11_21_48.png) We find that the corner points have the coordinates: 1: (0, 5) 2: (1, 2.5) 3: (6, 0) Now that we have identified the coordinates, we evaluate each of the pair of coordinates with the objective function z = 3x + 15y: 1: z = 3(0) + 15(5) = 0 + 75 = 75 2: z = 3(1) + 15(2.5) = 3 + 37.5 = 40.5 3: z = 3(6) + 15(0) = 18 + 0 = 18 Thus, the combination of x and y that minimizes z is: (x, y) = (6, 0) and the objective function value is $18. Did that help? otherwise try this video: https://www.youtube.com/watch?v=7r3utA7jLqU |