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In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same
- a)Minimum value
- b)Mean value
- c)Maximum value
- d)Upper limit value
Correct answer is option 'C'. Can you explain this answer?
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In a LPP if the objective function Z = ax + by has the same maximum va...
In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same maximum value .
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In a LPP if the objective function Z = ax + by has the same maximum va...
Explanation:
In a Linear Programming Problem (LPP), the objective function represents the quantity that needs to be maximized or minimized. The objective function is typically a linear combination of variables, and its value depends on the values of these variables.
In this given LPP, the objective function is Z = ax - by, where a and b are constants and x and y are decision variables.
The corner points of the feasible region are the extreme points of the region defined by the constraints. These corner points are obtained by solving the system of equations formed by the constraints.
If the objective function Z has the same maximum value on two corner points A and B of the feasible region, it means that the value of Z is equal at these two points, i.e., Z(A) = Z(B).
We are given that A and B are connected by a line segment. This line segment represents all the points lying between A and B.
Meaning of same maximum value:
When Z has the same maximum value at two corner points A and B, it implies that the value of Z is constant along the line segment joining A and B. This means that every point on this line segment will have the same maximum value of Z.
In other words, if we substitute the values of x and y from any point on the line segment into the objective function Z = ax - by, we will obtain the same maximum value as at the corner points A and B.
Hence, every point on the line segment joining the two corner points A and B will give the same maximum value of the objective function Z.
Therefore, the correct answer is option 'C' - every point on the line segment joining these two points gives the same maximum value.
In a Linear Programming Problem (LPP), the objective function represents the quantity that needs to be maximized or minimized. The objective function is typically a linear combination of variables, and its value depends on the values of these variables.
In this given LPP, the objective function is Z = ax - by, where a and b are constants and x and y are decision variables.
The corner points of the feasible region are the extreme points of the region defined by the constraints. These corner points are obtained by solving the system of equations formed by the constraints.
If the objective function Z has the same maximum value on two corner points A and B of the feasible region, it means that the value of Z is equal at these two points, i.e., Z(A) = Z(B).
We are given that A and B are connected by a line segment. This line segment represents all the points lying between A and B.
Meaning of same maximum value:
When Z has the same maximum value at two corner points A and B, it implies that the value of Z is constant along the line segment joining A and B. This means that every point on this line segment will have the same maximum value of Z.
In other words, if we substitute the values of x and y from any point on the line segment into the objective function Z = ax - by, we will obtain the same maximum value as at the corner points A and B.
Hence, every point on the line segment joining the two corner points A and B will give the same maximum value of the objective function Z.
Therefore, the correct answer is option 'C' - every point on the line segment joining these two points gives the same maximum value.
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In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the samea)Minimum valueb)Mean valuec)Maximum valued)Upper limit valueCorrect answer is option 'C'. Can you explain this answer?
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In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the samea)Minimum valueb)Mean valuec)Maximum valued)Upper limit valueCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the samea)Minimum valueb)Mean valuec)Maximum valued)Upper limit valueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the samea)Minimum valueb)Mean valuec)Maximum valued)Upper limit valueCorrect answer is option 'C'. Can you explain this answer?.
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