Question

Corner points of the feasible region for an LPP are (0,3), (5, 0), (6, 8) and (0, 8). Let Z=4x+6y be the objective function. The minimum and maximum value of Z occurs at​

Answer 1

Answer:

The minimum and maximum of the objective function are 18 and 72  respectively.

Step-by-step explanation:

Given the corner points of the feasible region are (0,3), (5,0), (6,8) and (0,8).

The objective function is $z=4x+6y$

The value of $z$ at each of the corner points is given by,

$(0,3) \implies \ \ z=4\times 0+6\times 3=18\\(5,0) \implies \ \ z=4\times 5+6\times 0=20\\(6,8) \implies \ \ z=4\times 6+6\times 8=24+48=72\\(0,8) \implies \ \ z=4\times 0+6\times 8=48$

So the maximum value of the objective function is 72 and minimum value is 18.

Answer 2

SOLUTION

GIVEN

• Corner points of the feasible region for an LPP are (0,3), (5, 0), (6, 8) and (0, 8).

• Let Z = 4x + 6y be the objective function.

TO DETERMINE

The minimum and maximum value of Z occurs at

EVALUATION

Here the given objective function is

Z = 4x + 6y

Corner points of the feasible region are (0,3), (5, 0), (6, 8) and (0, 8)

Now we have

$\sf Z_{(0,3)} = (4 \times 0) + (6 \times 3) = 0 + 18 = 18$

$\sf Z_{(5,0)} = (4 \times 5) + (6 \times 0) = 20 + 0 = 20$

$\sf Z_{(6,8)} = (4 \times 6) + (6 \times 8) = 24+ 48 = 72$

$\sf Z_{(0,8)} = (4 \times 0) + (6 \times 8) = 0 + 48 = 48$

• Minimum value of Z occurs at (0,3) and minimum value is 18

• Maximum value of Z occurs at (6,8) and minimum value is 72

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