Algebra

Linear Programming

Medium

common

The objective function of an LPP is $z = ax + by$ . If the maximum value of the objective function is 180, which occurs at two points (15,15) and (0,20), then which one of the following is true?

$a = 3, b = 9$

$a = 9, b = 3$

$a = 6, b = 6$

$a = 4, b = 8$

✅ Correct Option: 1

The objective function is $z = ax + by$ with maximum value 180 occurring at points $(15, 15)$ and $(0, 20)$ .

Since the maximum value is 180 at point $(15, 15)$ :

$z = ax + by$

$180 = a(15) + b(15)$

$180 = 15a + 15b$

$12 = a + b$ ... ①

Since the maximum value is also 180 at point $(0, 20)$ :

$z = ax + by$

$180 = a(0) + b(20)$

$180 = 20b$

$b = 9$ ... ②

From equation ①:

$a + b = 12$

$a + 9 = 12$

$a = 3$

Therefore, $a = 3$ and $b = 9$ .

The answer is option 1.

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CUET Mathematics Past Year Questions (Topic-Wise)

The objective function of an LPP is $z = ax + by$ . If the maximum value of the objective function is 180, which occurs at two points (15,15) and (0,20), then which one of the following is true?