A factory produces two kinds of notebooks: A and B. Profit per unit is ₹30 for A and ₹45 for B. The available resources each day are described by: 1. (5A+3Ble 90) (paper) 2. (2A+4Ble 64) (labour) If (A,Bge 0), find the production quantities that maximise the total profit using the graphical method and state the maximum profit.

Step-by-step solution

1. Identify the two constraints and the non‑negativity conditions.
2. Plot the lines (5A+3B=90) and (2A+4B=64) and determine the feasible region bounded by the axes and the two lines.
3. Compute the intersection of the two lines by solving (\begin{cases}5A+3B=90\2A+4B=64end{cases}) to get ((A,B)=(12,10)).
4. Find the other corner points of the feasible region: ((0,16)) from (5A+3B=90) and (A=0); ((18,0)) from (2A+4B=64) and (B=0); ((0,0)).
5. Evaluate the profit (P=30A+45B) at each corner: (P(12,10)=810), (P(0,16)=720), (P(18,0)=540), (P(0,0)=0).
6. Select the corner with the highest profit, giving (A=12,;B=10) and ($P_{max}$=₹810).

Concept tested: Graphical solution of 2‑variable LP

Published 7 October 2026 · How this solution was prepared and checked