Question

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded.

Maximize p=x+ysubject to

x+3y≤4

3x+y≤4

x≤0

y≤0

Answer 1

P = 4

Explanation:

The LP is:

Maximize p = x+y

x+3y≤4

3x+y≤4

x ≥ 0

y ≥ 0

Solving graphically using the geogebra graphing calculator which is attached, the points are A(0, 4), B(0, 1.33), C(1.33, 0), D(4, 0) and E(1, 1)

The maximum objective is:

For point A(0, 4): Maximize p = x + y = 0 + 4 = 4

For point B(0, 1.33): Maximize p = x + y = 0 + 1.33 = 1.33

For point C(1.33, 0): Maximize p = x + y = 1.33 + 0 = 1.33

For point D(4, 0): Maximize p = x + y = 4 + 0 = 4

For point E(1, 1): Maximize p = x + y = 1 + 1 = 2

Hence, the maximum point is at A(0, 4) which gives P = 4