ExamBro
ExamBro
COMEDK · Maths · 28. Indefinite Integration

The corner points of the feasible region determined by the system of linear constraints are \((0,3),(1,1)\) and \((3,0)\). If objective function is \(Z=p x+q y, p, q>0\) then the condition on \(p\) and \(q\) so that the minimum of \(Z\) occurs at \((3,0)\) and \((1,1)\) is

  1. A \(p=2 q\)
  2. B \(p=\dfrac{q}{2}\)
  3. C \(p=3 q\)
  4. D \(3 p=q\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(p=\dfrac{q}{2}\)

Step-by-step Solution

Detailed explanation

The objective function is \(Z = px + qy\). The values of \(Z\) at the corner points are: At \((0, 3)\), \(Z = p(0) + q(3) = 3q\). At \((1, 1)\), \(Z = p(1) + q(1) = p + q\). At \((3, 0)\), \(Z = p(3) + q(0) = 3p\). For the minimum of \(Z\) to occur at both \((3, 0)\) and…