Question

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.)
Maximize p = x + 2y subject to
x + 3y ≤ 22
2x + y ≤ 14
x ≥ 0, y ≥ 0.
p = (x,y) =

Answer 1

Answer:

(x,y)=(0,7.333)

Step-by-step explanation:

We are required to:

Maximize p = x + 2y subject to

• x + 3y ≤ 22
• 2x + y ≤ 14
• x ≥ 0, y ≥ 0.

The graph of the lines are plotted and attached below.

From the graph, the vertices of the feasible region are:

• (0,7.333)
• (4,6)
• (0,0)
• (7,0)

At (0,7.333), p=0+2(7.333)=14.666

At (4,6), p=4+2(6)=4+12=16

At (0,0), p=0

At (7,0), p=7+2(0)=7

Since 14.666 is the highest, the maximum point of the feasible region is (0,7.333).

At x=0 and y=7.333, the function p is maximized.