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 constraints to the LPP are:
A. \(3x + 2y \le 720\)
B. \(2x + 3y \le 720\)
C. \(x + y \le 300\)
D. \(x \ge 0\) and \(y \ge 0\)
E. \(x + y \ge 300\)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → B, C, D only
At most 300 sets a week:
\(x + y \le 300\)
The cost limit of Rs. 6,48,000:
\(1800x + 2700y \le 648000\)
Dividing by 900:
\(2x + 3y \le 720\)
The numbers of sets cannot be negative: \(x \ge 0,\ y \ge 0\).
So the constraints are \(2x + 3y \le 720\), \(x + y \le 300\), \(x \ge 0\) and \(y \ge 0\).
Checking the statements
(A) \(3x + 2y \le 720\) — Incorrect. The costs give 2x + 3y, not 3x + 2y.
(B) \(2x + 3y \le 720\) — Correct. This is the cost limit divided by 900.
(C) \(x + y \le 300\) — Correct. At most 300 sets a week.
(D) \(x \ge 0\) and \(y \ge 0\) — Correct. The numbers of sets are non-negative.
(E) \(x + y \ge 300\) — Incorrect. “At most 300” means ≤ 300.