The corner points of the bounded feasible region associated with the LPP: Maximize Z=px+qy, p,q>0 are (0, 0), (3.5, 0), (112/59, 135/59) and (0, 3). If the optimum value of Z occurs at both (112/59, 135/59) and (0, 3), then Option 1: 3q = 5p Option 2: 8p = 3q Option 3: 5p = 8q Option 4: 3p = 5q

Answer: 8p = 3q. Solution: When the maximum value of Z occurs at two corner points, Z has the same value at both points. At point (112/59, 135/59): Z = p * 112/59 + q * 135/59 Z = 112p/59 + 135q/59 At point (0, 3): Z = p * 0 + q * 3 Z = 3q Since both points give the maximum value: 112p/59 + 135q/59 = 3q 112p/59 = 3q - 135q/59 112p/59 = 177q/59 - 135q/59 112p/59 = 42q/59 112p = 42q 8p = 3q Therefore, the relationship between p and q is 8p = 3q.

Algebra

Linear Programming

Hard

common

The corner points of the bounded feasible region associated with the LPP: Maximize $Z=px+qy$ , $p,q>0$ are $(0, 0)$ , $(3.5, 0)$ , $\left(\frac{112}{59}, \frac{135}{59}\right)$ and $(0, 3)$ . If the optimum value of Z occurs at both $\left(\frac{112}{59}, \frac{135}{59}\right)$ and $(0, 3)$ , then

$3q = 5p$

$8p = 3q$

$5p = 8q$

$3p = 5q$

✅ Correct Option: 2

When the maximum value of $Z$ occurs at two corner points, $Z$ has the same value at both points.

At point $\left(\frac{112}{59}, \frac{135}{59}\right)$ :

$Z = p \cdot \frac{112}{59} + q \cdot \frac{135}{59}$

$Z = \frac{112p}{59} + \frac{135q}{59}$

At point $(0, 3)$ :

$Z = p \cdot 0 + q \cdot 3$

$Z = 3q$

Since both points give the maximum value:

$\frac{112p}{59} + \frac{135q}{59} = 3q$

$\frac{112p}{59} = 3q - \frac{135q}{59}$

$\frac{112p}{59} = \frac{177q}{59} - \frac{135q}{59}$

$\frac{112p}{59} = \frac{42q}{59}$

$112p = 42q$

$8p = 3q$

Therefore, the relationship between $p$ and $q$ is $8p = 3q$ .

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A. Maximum distance covered in one hour is 30 km

B. The distance covered at speed of 25km/hr is 50/3 km

C. The distance covered at speed of 25km/hr is $\frac{25}{2}$ km

D. The distance covered at speed of 40km/hr is $\frac{75}{4}$ km

Choose the correct answer from the options given below:

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subject to the constraints:

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Solution

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