Solve this LP using the simplex method.

1.

Max z = 2x1 + x2 + 2x3

Subject to 4x1 + 3x2 + 8x3 12 4x1 + x2 + 12x3 8 4x1 - x2 + 3x3 8 x1, x2, x3 0

2.

Min z = 2x1+ x2

Subject to 3x1+ x2 = 3* 4x1+ 3x2 6 x1+ 2x2 3 x1, x2 0

*Constraints with "=" sign in simplex iteration are added with artificial variables, so that it becomes 3x1 + x2 + A1 = 3

3.

(From Winston, 2004)

Min z = 5x1+ x2

Subject to 2x1+ x2 6 x1+ x2 4 2x1+ 10x2 20 x1, x2 0

4. (From Winston, 2004)

Bevco manufactures an orange-flavored soft drink called Oranj by combining orange soda and orange juice. Each ounce of orange soda contains 0.5 oz of sugar and 1 mg of vitamin C. Each ounce of orange juice contains 0.25 oz of sugar and 3 mg of vitamin C. It costs Bevco 2 to produce an ounce of orange soda and 3 to produce an ounce of orange juice. Bevcos marketing department has decided that each 10-oz bottle of Oranj must contain at least 20 mg of vitamin C and at most 4 oz of sugar. Use linear programming to determine how Bevco can meet the marketing departments requirements at minimum cost!