Question

1. Solve the following LP problem. Solve graphically. Maximize profit = ​9x1​+​ 7x2 Subject to:​​2x1​+ ​1x2​≤​40...

1. Solve the following LP problem. Solve graphically.
Maximize profit = ​9x1​+​ 7x2
Subject to:​​2x1​+ ​1x2​≤​40
​x1 ​+ ​3x2​≤​30
x1, x2​≥​0

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Answer #1

1. To draw constraint 2xx Treat it as 2x1 = 40 When x1 = 0 then x2 = ? 40(1) 2(0) +x2 = 40 When x2 = 0 then x1 = ? 2x1+(0)-40 2x1 40 40 x1 0 20 첫40

2. To draw constraint x1+32s 30(2) reat it as x1 +3x2-30 When X1 = 0 then x2 = ? (0) 3x2 = 30 30 When x2 = 0 then x1 = ? x1 + 3(0) = 30 x1 0 30 2 10 0

x y -30 (7, 31) 10 15

The value of the o function at each of these extreme s is as follows Extreme Point Coordinates Objective function value Lines through Extreme Point x1x 900)+T0)-0 9(20)+7(0) 180 9(18) + 7(4) = 190 9 710)-70 A(20, 0) B(13, 4) 2+3x230 2→x1 +3x2 30 3x 0 C(0, 10) The maximum value of the objective function 190 occurs at the extreme point (18, 4) Hence. the optimal solution to the given LP problem is : x1 = 18, x2 = 4 and max: = 190

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1. Solve the following LP problem. Solve graphically. Maximize profit = ​9x1​+​ 7x2 Subject to:​​2x1​+ ​1x2​≤​40...
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