TOPIC: LINEAR PROGRAMMING 1.) Solve the following nonstandard maximum problem: Maximize P = 3x, + X2 subject to the constraints: X1+ X2 58 5x1 + 3x2 2 36 7x1 + 4x2 2 14 x1 20, X2 2 0 The maximum of the objective function is reached at the point: Choices: a. X1 = 6 , X2 = 2 b. x1 = 2 , X2 = 6 C. X1 = 11 , X2 = 2. d. X1 = 2 , X2 = 2 2.) The maximum problem is not in standard form. Determine if the problem can be modified so as to be in standard form. If it can, write the modified version. Maximize P = X1 + X2 subject to the constraints 5x1 - 6X2 $ - 11 X1+ X2 X120, X2 20 Choices: Maximize P = X1 + X2 subject to the constraints Maximize P = X1 + X2 subject to the constraints 5x1 - 6X2 $ - 11 O 5x1 - 6X2 $ 11 -X1-X2 5 -6 O X1+ X2 $ 6 X120, X2 20 X120, X2 20 b. The maximum problem cannot be modified to be in standard form. O e. Maximize P = X1 + X2 subject to the constraints C. Maximize P = X1 + X2 subject to the constraints -5x1 + 6X2 2 11 -5x1 + 6X2 $ 11 O O X1+X2 56 X1 + X2 $6 X120, X2 20 X120, X2 20 3.) The maximum problem is not in standard form. Determine if the problem can be modified so as to be in standard form. If it can, write the modified version. Maximize P = 3X1 + X2 + 8X3 subject to the constraints -X1+ X2 + X3 2 - 10 3x1 - 8X2 2 - 15 X3 $3 X1 20, X2 20, x320 Choices: a. Maximize P = 3x1 + X2 + 8X3 subject to the constraints d. Maximize P = 3X1 + X2 + 8X3 subject to the constraints X1 -X2 -X3 2 10 X1+ X2 + X3 $ 10 -3x1 + 8X2 2 15 O -3x1 + 8X2 $ 15 O X3 $3 X1 20, X2 20, X320 X3 3 X120, X2 20, X320 b. The maximum problem cannot be O modified to be in standard form. e. Maximize P = 3x1 + X2 + 8X3 subject to the constraints C. Maximize P = 3X1 + X2 + 8X3 subject to the constraints X1 + X2 + X3 2 -10 X1 -X2-X3 $ 10 -3x1 + 8X2 2 - 15 O -3x1 + 8X2 $ 15 O -X3 X1 20, X2 20, x320 X120, X2 20, X320