Question:
The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (0, 4), (4, 0), (2, 4) and (0, 5). If the maximum value of Z = ax + by where a, b > 0 occurs at both (2, 4) and (4, 0) then
The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (0, 4), (4, 0), (2, 4) and (0, 5). If the maximum value of Z = ax + by where a, b > 0 occurs at both (2, 4) and (4, 0) then
Updated On: Mar 27, 2026
- a = 2b
- 2a = b
- a = b
- 3a = b
Show Solution
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The Correct Option is A
Solution and Explanation
To solve for the relationship between a and b given that the maximum value of Z = ax + by occurs at both (2, 4) and (4, 0), follow these steps:
- Calculate the value of Z at point (2, 4):
Z1 = a(2) + b(4) = 2a + 4b. - Calculate the value of Z at point (4, 0):
Z2 = a(4) + b(0) = 4a. - Since both points provide the maximum value of Z, set Z1 equal to Z2:
2a + 4b = 4a. - Simplify the equation:
4b = 4a - 2a - Simplify further:
4b = 2a - Divide both sides by 2:
2b = a - Rearrange to find the relationship:
a = 2b
This shows that the correct relationship between a and b is a = 2b.
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