A company produces two products X and Y. The profit per unit of X is ₹50 and that of Y is ₹70. The resources available each day are described by the following constraints: 1. 3X + 2Y ≤ 60 2. 2X + 4Y ≤ 48 If X and Y must be non‑negative, determine the production quantities that maximise the total profit and state the maximum profit using the graphical method.
Answer
Produce 18 units of X and 3 units of Y for a maximum profit of ₹1110.
The correct answer is Produce 18 units of X and 3 units of Y for a maximum profit of ₹1110. — Select the corner giving the highest profit: (18,3) with ₹1110.
Step-by-step solution
- List the feasible region defined by the two inequalities and non‑negativity.
- Determine the corner points: (0,0), (0,12), (20,0), and the intersection of the two lines.
- Compute the intersection point by solving the equations 3X+2Y=60 and 2X+4Y=48 → X=18, Y=3.
- Calculate the profit at each corner: at (0,12) ₹840, at (20,0) ₹1000, at (18,3) ₹1110.
- Select the corner giving the highest profit: (18,3) with ₹1110.
Common mistake: Using an incorrect intersection point or mis‑computing the profit at a vertex
Concept tested: Graphical method for LP
Published · How this solution was prepared and checked
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