Question

The maximum value of \(Z = 4x+5y\), subject to the constraints \(3x+y\leq 15,3x+4y\leq 24,x\geq 0,y\geq 0\) is

• A. \(31\)
• B. \(30\)
• C. \(42\)
• D. \(47\)

Hint:

Check Z at each corner point of the feasible region.

Answer 1

The Correct Option is A

Step 1: Check feasibility:
$(4, 3)$: $3(4) + 3 = 15 \leq 15$ and $12 + 12 = 24 \leq 24$. Both hold, so it is a feasible corner.

Step 2: Compare values:
Corner values are $0, 20, 30, 31$. The largest is $31$.
The options $42$ and $47$ are not reached anywhere in the region.

Final Answer:
The maximum value of $Z$ is $31$, option (A). \[ \boxed{31} \]