The corner points of the bounded feasible region associated with the LPP: Maximize \(Z = px + qy,\ p, q \gt 0\) are (0, 0), (3.5, 0), \(\left(\displaystyle\frac{112}{59}, \frac{135}{59}\right)\) and (0, 3). If the optimum value of Z occurs at both \(\left(\displaystyle\frac{112}{59}, \frac{135}{59}\right)\) and (0, 3), then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(8p = 3q\)
If the optimum occurs at two corner points, Z has the same value at both of them:
\( \displaystyle Z\left(\frac{112}{59}, \frac{135}{59}\right) = Z(0, 3) \)
\( \displaystyle \frac{112p + 135q}{59} = 3q \)
\(112p + 135q = 177q\)
\(112p = 42q\)
Dividing by 14:
\(8p = 3q\)
NCERT Exemplar:
Linear Programming
