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# The Simplex Solution Method

minimize Z = 3x1 + 6x2 (cost, \$) subject to

( p r o d u c t i o n t i m e , d a y s ) ( c o n t r a c t , t o n s ) ( c h e r r y , t o n s ) ( o a k , t o n s ) x 1 , x 2 Ú 0 x 2 7 x 1 4 x 1 + x 2 Ú 5 3 x 1 + 2 x 2 1 8

Solve this model using the simplex method. 34. Solve the following linear programming model using the simplex method:

maximize Z = 10x1 + 5x2 subject to

x 1 , x 2 Ú 0 x 1 + 4 x 2 2 0 x 2 = 4 2 x 1 + x 2 Ú 1 0

35. Solve the following linear programming problem using the simplex method:

maximize Z = x1 + 2x2 - x

3

subject to

2 4x + x

3

1 x -x

2

2x1 + 4x2 + 3x

3

2 x1, x , x

3

• 40

• 20

• 60

Ú0

36. Solve the following linear programming problem using the simplex method:

maximize Z = x1 + 2x2 + 2x3 subject to

x 1 , x 2 , x 3 Ú 0 x 1 + x 2 - x 3 Ú 8 2 x 1 + x 2 + 5 x 3 = 2 0 x 1 + x 2 + 2 x 3 1 2

37. A farmer has a 40-acre farm in Georgia. The farmer is trying to determine how many acres of corn, peanuts, and cotton to plant. Each crop requires labor, fertilizer, and insecticide. The farmer has developed the following linear programming model to determine the number of acres of corn (x1), peanuts (x2), and cotton (x3) to plant to maximize profit:

maximize Z = 400x1 + 350x2 + 450x3 (profit, \$) subject to

( l a b o r , h r . ) ( f e r t i l i z e r , t o n s ) 4 x 1 + 3 x 2 + x 3 1 6 0 2 x 1 + 3 x 2 + 2 x 3 1 2 0

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