Solve the linear programming problem by the method of corners. Maximize P = 5x + 7y     subject to   2x  +  y  ≤  16   2x  +  3y  ≤  24       y  ≤    5   x ≥ 0, y ≥ 0   The maximum is P =  at  (x, y) =

Use the method of this section to solve the linear programming problem. Maximize  P = x + 2y subject to   2x  +  3y  ≤  12   −x  +  3y  =  3   x  ≥  0, y  ≥  0 The maximum is P =  at  (x, y) =                .

Solve the linear programming problem.   Maximize and minimize   z=4x+5y   Subject to 2x+y ≥ 10   x+2y ≥ 8   x, y ≥ 0 What is the minumum value of z? What are the coordinates of the corner point where the minimum value of z​ occurs? What is the maximum value of z? What are the coordinates of the corner point where the maximum value of z​ occurs?

Use the simplex method to solve the linear programming problem. Maximize: z = 2x₁ + x2 subject to: x₁ + 4x₂ ≤ 12 2x₁ + 6x₂ ≤ 4 X₁ + 2x2 ≤ 4 with x₁ ≥ 0, x₂ ≥ 0. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The maximum is when x₁ = x₂ = , S₁ = S2 = and S3 = B. There is no maximum solution to this linear programming problem.