Question

The minimum value of \(Z=7x+8y\) subject to \(3x+4y\le24,\ x\ge0,\ y\ge0\) is

• A. \(56\)
• B. \(48\)
• C. \(0\)
• D. \(-12\)

Hint:

For "$\le$" constraints with $x,y\ge0$, the origin is feasible; check it first for minimization.

Answer 1

The Correct Option is C

All coefficients in \(Z\) are positive and the origin \((0,0)\) is feasible (\(0\le24\)). Therefore the smallest value occurs at \((0,0)\): \(Z=0\).