Set up the simplex matrix used to solve each linear programming problem. Assume all variables are nonnegative.
1. Maximize f = 3x + 7y subject to
2x + 5y ≤400
x + 2y ≤175
2. Maximize f = x + 3y subject to
5x + y ≤ 50
x + 2y ≤ 50
3. Maximize f = 2x + 5y + 2z subject to
2x + 7y + 9z ≤ 100
6x + 5y + z ≤ 145
x + 2y + 7z ≤ 90
4. Maximize f = 3x + 5y + 11z subject to
2x + 3y + 4z ≤ 60
x + 4y + z ≤ 48
5x + y + z ≤ 48