A manufacturing company makes two types of television sets; one is black and white and the other is colour. The company has resources to make at most 300 sets a week. It takes Rs. 1800 to make a black and white set and Rs. 2700 to make a coloured set. The company can spend not more than Rs. 6,48,000 a week to make television sets. It makes a profit of Rs. 510 per black and white set and Rs. 675 per coloured set. Assuming x and y respectively are the number of black and white, and coloured sets made each week, answer the questions:
The corner points of feasible region are:
A. (0, 240)
B. (0, 0)
C. (300, 0)
D. (120, 180)
E. (180, 120)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, B, C, E only
The feasible region is given by \(x + y \le 300\), \(2x + 3y \le 720\), \(x \ge 0\), \(y \ge 0\).
On the axes:
\(x + y = 300\) meets the x-axis at (300, 0) and the y-axis at (0, 300)
\(2x + 3y = 720\) meets the x-axis at (360, 0) and the y-axis at (0, 240)
So the region reaches (300, 0) on the x-axis and (0, 240) on the y-axis. The two lines meet where
\(2x + 3y - 2(x + y) = 720 - 600\)
\(y = 120,\quad x = 180\)
So the corner points are (0, 0), (300, 0), (180, 120) and (0, 240).
Checking the statements
(A) (0, 240) — Correct. Where 2x + 3y = 720 meets the y-axis.
(B) (0, 0) — Correct. The origin is a corner.
(C) (300, 0) — Correct. Where x + y = 300 meets the x-axis.
(D) (120, 180) — Incorrect. 2(120) + 3(180) = 780 > 720, so it is not even feasible.
(E) (180, 120) — Correct. The two lines meet here.