Question

For linear programming problem, the objective function is \( z = px + qy \), \( p,q>0 \). If at the corner points \( (0,10) \) and \( (5,5) \), the value of \( z \) are 90 and 60 respectively, then the relation between \( p \) and \( q \) is _____

• A. \( p = 3q \)
• B. \( q = 2p \)
• C. \( q = 3p \)
• D. \( p = 2q \)

Hint:

Plug given corner values into objective function to form equations.

Answer 1

The Correct Option is C

Concept: Substitute coordinates into objective function.
Step 1: Use point (0,10). \[ z = 10q = 90 \Rightarrow q = 9 \]
Step 2: Use point (5,5). \[ 5p + 5q = 60 \] \[ 5p + 45 = 60 \] \[ 5p = 15 \Rightarrow p = 3 \]
Step 3: \[ q = 3p \]