Solve the linear programming problem by the method of corner

Solve the linear programming problem by the method of corners.

The maximum is P =

at (x, y) =

SOLUTION

The corner points are obtained by solving

x + y = 10 ......... (1)

3x + y = 12 ....... (2)

- 2x + 3y = 13 ...... (3)

Solving (1) and (2): x = 1, y = 9 ........ (4)

Solving (1) and (3): x = 3.4, y = 6.6 ........ (5)

Solving (3) and (2): x = 23/11, y = 64/11 ........ (6)

Thus, the corner points are P1 = (1, 9), P2 = (3.4, 6.6) and P3 = (23/11, 64/11)

Substituting these points in the objective function, value of P = 49 at P1, 46.6 at P2 and 37.5 at P3.

Since maximum is 49, MAX P = 49 at (1, 9) ANSWER