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Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empt...

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.)

a)Maximize p = 3x + 2y subject to

−4x+y≥10

x+3y≤12

x ≥ 0, y ≥ 0

p=

(x,y)=

b) Maximize and minimize p = x + 2y subject to

x + y 6
x + y 8
x y 6
x y

−6.

minimum:

p=

(x,y)=

maximum:

p=

(x,y)=

c) Maximize p = x − 2y subject to

x + 3y 7
x 4y 0
6x 3y 0
x ≥ 0, y ≥ 0

p=

(x,y)=

0 0
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