Question

$A $ dealer wishes to purchase table fans and ceiling fans. He has $₹\, 57, 600$ to invest, and has space to store $40$ items. $A$ table fan costs $₹ \,750$ and ceiling fan costs $₹ \,900$. He can make profits of $₹ \,70$ and $₹ \,90$ by selling a table fan and ceiling fan respectively. Assuming that he can sell all the fans that he can buy, formulate this problem as $L P P$, to maximize the profit.

• A. Maximize $Z = 70x + 90y$
  Subject to $x + y \le 40, 750x + 900y \le 57600$
  $ x \le 0,y \ge 0$
• B. Maximize $Z = 70x + 90y$
  Subject to $x + y \le 40, 750x + 900y \le 57600$
  $ x \ge 0,y \le 0$
• C. Maximize $Z = 70x + 90y$
  Subject to $x + y \le 40, 750x + 900y \le 57600$
  $ x \ge 0,y \ge 0$
• D. Maximize $Z = 70x + 90y$
  Subject to $x + y \le 40, 750x + 900y \le 57600$
  $ x \le 0,y \le 0$

Answer 1

Answer: (C)

Let the dealer buys$ 'x'$ table fans and $'y'$ ceiling fans.
Profit on one table fan is $₹ 70$
$ \therefore $ Profit on $x$ table fans is $₹ 70x$
Profit on one ceiling fan is $₹ 90$
$ \therefore $ Profit on $y$ ceiling fans is $₹ 90y$
$ \therefore $ Total profit, $Z = 70x + 90y$
He has space to store $40$ items.
$ \therefore x + y \le 40$
Cost of one table fan is $₹ 750 $
$ \therefore $Cost of $x$ table fans is $₹ 750x$
Cost of one ceiling fan is $ ₹ 900$
$ \therefore $ Cost of $y$ ceiling fans is $₹ 900y$
$ \therefore $ Total cost $= 750x + 900y$
He has $₹ 57,600$ to invest.
$ \therefore $ $750x + 900y \le57600$
$ \therefore $ Given problem can be formulated as
Maximize $Z = 70x + 90y$
Subject to, $x + y \le 40,750x + 900y \le 57600, x\ge 0, y \ge 0$.