A fruit seller has Rs. 2400 to buy mangoes and apples. Mangoes cost Rs. 60 per kg and apples cost Rs. 120 per kg, and his cart can carry at most 30 kg. He makes a profit of Rs. 10 per kg on mangoes and Rs. 15 per kg on apples, and he sells all that he buys. The maximum profit he can make is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 350
Let him buy x kg of mangoes and y kg of apples. Then
Maximise \(Z = 10x + 15y\)
subject to
\(60x + 120y \le 2400\), that is, \(x + 2y \le 40\)
\(x + y \le 30\)
\(x \ge 0, \; y \ge 0\)
The lines \(x + 2y = 40\) and \(x + y = 30\) meet where
\(y = 10, \; x = 20\)
The corner points are (0, 0), (30, 0), (20, 10) and (0, 20). Values of Z:
\(Z(30, 0) = 300\)
\(Z(20, 10) = 200 + 150 = 350\)
\(Z(0, 20) = 300\)
So the maximum profit is Rs. 350, with 20 kg of mangoes and 10 kg of apples.
Why the other options are incorrect
Option (1) Rs. 300 — Incorrect. This is the profit from mangoes only or apples only; buying both gives more.
Option (3) Rs. 400 — Incorrect. No corner gives Rs. 400; the largest corner value is Rs. 350.
Option (4) Rs. 450 — Incorrect. This needs 30 kg of apples, costing Rs. 3600, which is more than Rs. 2400.