Question

The vertices of the feasible region of L.P.P. are A (6, 0), B (3, 1), C (1, 3), D (0, 6), E (7, 0), F (0, 7), G (7, 7) and its objective function Z = 2000 x + 1600 y. Find maximum value of objective function Z.​

Answer 1

Answer:

Step-by-step explanation:

Z= 25,200

Given,

Z = 2000 x + 1600 y

A(6,0), B(3,1), C(1,3), D(0,6), E(7,0), F(0,7), G(7,7)

To Find,

Maximum value of objective function Z.

Solution,

The value of objective function Z = 2000 x + 1600 y at

• A(6,0)

        Z(A)= 2000(6) + 1600(0)

               = 12,000

• B(3,1)

• Z(B)= 2000(3) + 1600(1)
•        = 6000 + 1600
•        =
• 7,600
• C(1,3)

         Z(C)= 2000(1) + 1600(3)

•         = 2000 + 4800
•         =
• 6,800
• D(0,6)
•  Z(D)= 2000(0) + 1600(6)
•          =
• 9,600
• E(7,0)
•  Z(E)= 2000(7) + 1600(0)
•         = 14,000

• F(0,7)

• Z(F)= 2000(0) + 1600(7)

               = 11,200

• G(7,7)

• Z(G)= 2000(7) + 1600(7)
•        = 14000 + 11200
•        =
• 25,200

Therefore, The maximum value of objective Z = 25,200 at vertices G(7,7).