Suppose that in an optimization problem, the objective function is given by u(X

Question

Suppose that in an optimization problem, the objective function is given by u(X1 , X2) =10+2X1+4X2.. Suppose that there are two optimal solutions, and that one of them is (X1 , X2 )=(1,2). What must be the value of the objective function at the other optimal solution?

It cannot possibly be determined without knowledge of what the constraints are.

20.

10.

Even if we knew what the constraints are, we'd need to know the actual numbers themselves to determine the answer.

It cannot possibly be determined without knowledge of what the constraints are.

20.

10.

Even if we knew what the constraints are, we'd need to know the actual numbers themselves to determine the answer.

Explanation / Answer

if the objective funtion has two optimal solutions and if they are not equal i.e value1>value2 or value2<value2

either point 1 or point 2 will be optimal solution

so if the objective funtion has two optimal solutions then value at both the points should be equal

gievnt that on optimal solution is  (X1 , X2 )=(1,2)

value at (1,2) is U(X1,X2) = 10+2*1+4*2 = 10+2+8 = 20

so value at other optimal should be equal to 20 (b)

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