A tea company packs masala tea and green tea in cartons. A carton of masala tea needs 2 hours of blending and 1 hour of packing, and a carton of green tea needs 1 hour of blending and 2 hours of packing. In a month 100 hours of blending and 80 hours of packing are available. The profit is Rs. 30 on a carton of masala tea and Rs. 40 on a carton of green tea, and all the cartons are sold. Match List-I with List-II.
| List-I | List-II | ||
|---|---|---|---|
| (A) | Number of corner points of the feasible region | (I) | 60 |
| (B) | Maximum profit (in Rs.) | (II) | 2000 |
| (C) | Greatest profit (in Rs.) if only green tea is packed | (III) | 4 |
| (D) | Total number of cartons in the most profitable plan | (IV) | 1600 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
Let x cartons of masala tea and y cartons of green tea be packed in a month. Then
Maximise \(Z = 30x + 40y\)
subject to
\(2x + y \le 100\) (blending)
\(x + 2y \le 80\) (packing)
\(x \ge 0,\ y \ge 0\)
The two lines meet where, doubling the second and subtracting the first,
\(3y = 60\)
\(y = 20,\ x = 40\)
The corner points are (0, 0), (50, 0), (40, 20) and (0, 40). Values of Z:
\(Z(0, 0) = 0\)
\(Z(50, 0) = 1500\)
\(Z(40, 20) = 1200 + 800 = 2000\)
\(Z(0, 40) = 1600\)
(A) Number of corner points
The region has the 4 corners listed, so it is (III) 4.
(B) Maximum profit
The largest value is at (40, 20), so it is (II) 2000.
(C) Greatest profit if only green tea is packed
With \(x = 0\), packing allows at most 40 cartons, and \(40 \times 40 = 1600\), so it is (IV) 1600.
(D) Total number of cartons in the most profitable plan
\(40 + 20 = 60\) cartons, so it is (I) 60.