Solve the following linear programming problem by the simplex method. Show the solution.

1. A hog raiser is mixing two types of grains A and B. Each unit of grain A costs 50 and contains 20 grams of fat and 10 grams of protein. Each unit of grain B costs 80 and contains 30 grams of fat and 30 grams of protein. The hog raiser wants each unit of the final product to yield at least 180 grams of fat and at least 120 grams of protein. How many units of each type of grain should he use to maximize his sales?

2. Minimize Z = 8X₁ + 6X₂

Subject to:

3x₁ + 4x₂ >= 6

5x₁ + 2x₂ <= 10

x₁+ 4x₂ <= 4

x, y >=0