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 maximum profit per week is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 1,72,800
The feasible region of \(x + y \le 300\), \(2x + 3y \le 720\), \(x, y \ge 0\) has corners (0, 0), (300, 0), (180, 120) and (0, 240). The maximum of z = 510x + 675y is at a corner point:
\(z(0, 0) = 0\)
\(z(300, 0) = 153000\)
\(z(180, 120) = 91800 + 81000 = 172800\)
\(z(0, 240) = 162000\)
The maximum profit is Rs. 1,72,800 a week, with 180 black and white sets and 120 coloured sets.