The given figure illustrates the graph of the set of feasible points of a linear

Question

The given figure illustrates the graph of the set of feasible points of a linear programming problem. Find the minimum and maximum values of an objective function z = 2x + 5y. The minimum value of the objective function is 7 and the maximum value is 54. The minimum value of the objective function is 14 and the maximum value is 81. The objective function has the maximum value 54 and doesn't have a minimum value. The objective function has the minimum value 7 and doesn't have a maximum value. The minimum value of the objective function is 14 and the maximum value is 54.

Explanation / Answer

As the region is closed , therefore it is bounded.

To find the maximum and Minimum value of the objective function , we need to evaluate the objective function at each vertex.

The given vertices are (2,7) , (7,8) , (2,2) , (8,1)

Objective function is given by z(x,y) = 2x + 5y

At (2,7) ,the objective function z(2,7) = 2(2) + 5(7) = 4 + 35 = 39

At (7,8) ,the objective function z(7,8) = 2(7) + 5(8) = 14 + 40 = 54

At (2,2) ,the objective function z(2,2) = 2(2) + 5(2) = 4 + 10 = 14

At (8,1) ,the objective function z(8,1) = 2(8) + 5(1) = 16 + 5 = 80

Therefore the Maximium value of the objective function z = 2x + 5y is equal to 54 at (7,8)

And the Minimum value of the objective function z = 2x + 5y is equal to 14 at (2,2)

So fifth option is correct.

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