HW 2 Solutions

HW 2 Solutions - Two-Variable LP Homework Solutions STOR...

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Unformatted text preview: Two-Variable LP Homework Solutions STOR 112 35 points written work + 10 points computer work 1. (5 points) Consider the following linear program: max p = x + 2 y subject to 30 x + 20 y ≤ 600 . 1 x + 0 . 4 y ≤ 4 . 2 x + 0 . 3 y ≤ 4 . 5 x,y ≥ (a) Graph the feasible region. (b) Make a table of the extreme points. For each point, list the objective value at that point and which constraints are binding at that point. Indicate which corner point is the optimal one. Solution. The corner points are (0,0); (20,0); (0,10); (18,3); and (12,7). The last two are obtained by solving the systems of equations created by the two constraints. Point p = x + 2 y Constraints (0,0) x = 0 ,y = 0 (20,0) 20 30 x + 20 y = 600 ,y = 0 (0,10) 20 . 1 x + 0 . 4 y = 4 ,x = 0 (18,3) 24 . 2 x + 0 . 3 y = 4 . 5 , 30 x + 20 y = 600 (12,7) 26 . 1 x + 0 . 4 y = 4 , . 2 x + 0 . 3 y = 4 . 5 Since we wish to maximize p, we choose the point with the largest value, which is (12,7). 2. (15 points) Podunk Institute of Technology’s Math Department offers two courses: Finite Math and Applied Calculus. Each section of Finite Math has 60 students, and each section of Applied Calculus has 50. The department is allowed to offer up to 110 sections total. Furthermore, no more than 6000is allowed to offer up to 110 sections total....
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HW 2 Solutions - Two-Variable LP Homework Solutions STOR...

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