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:
A feasible solution is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (180, 120)
A feasible solution must satisfy every constraint: \(x + y \le 300\), \(2x + 3y \le 720\), \(x, y \ge 0\).
\((120, 180)\): \(2(120) + 3(180) = 780 \gt 720\), not feasible
\((180, 120)\): \(180 + 120 = 300\) and \(2(180) + 3(120) = 720\), feasible
\((0, 300)\): \(3(300) = 900 \gt 720\), not feasible
\((360, 0)\): \(360 \gt 300\), not feasible
Only (180, 120) satisfies all the constraints; it is the corner where both lines meet.