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 $LPP$, 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${}^{\prime }{x}^{\prime }$ table fans and ${}^{\prime }{y}^{\prime }$ 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.
$\therefore$ $750x+900y\le 57600$
$\therefore$ Given problem can be formulated as
Maximize $Z=70x+90y$
Subject to, $x+y\le 40,750x+900y\le 57600,x\ge 0,y\ge 0$.