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( i n s e c t i c i d e , t o n s ) ( a c r e s ) x 1 , x 2 , x 3 Ú 0 x 1 + x 2 + x 3 4 0 3 x 1 + 2 x 2 + 4 x 3 1 0 0

Solve this model using the simplex method. 38. Solve the following linear programming model (a) graphically and (b) using the simplex method:

maximize Z = 3x1 + 2x2 subject to

x 1 , x 2 Ú 0 x 1 + x 2 Ú 2 x 1 + x 2 1

39. Solve the following linear programming model (a) graphically and (b) using the simplex method:

maximize Z = x1 + x2 subject to

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

40. Solve the following linear programming model using the simplex method:

1 2 x +x +x

3

1 2 2x + x + x

3

1 x +x

2

x

3

x1, x2, x

3

maximize Z = 7x1 + 5x2 + 5x subject to

• 25

• 40

• 25

• 6

Ú0

3

41. Solve the following linear programming model using the simplex method:

minimize Z = 15x1 + 25x2

subject to

3x1 + 4x x 1 , x 3x1 + 2x Ú 12 Ú6 9 2 2 2 2 Ú 0 2 x 1 + x

42. The Old English Metal Crafters Company makes brass trays and buckets. The number of trays (x1) and buckets (x2) that can be produced daily is constrained by the availability of brass and labor, as reflected in the following linear programming model:

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