Question

A furniture manufacturer produces tables and bookshelves made up of wood and steel. The weekly requirement of wood and steel is given as below.

The weekly availability of wood and steel is $450$ and $100$ units respectively. Profit on a table is $₹ 1000$ and that on a bookshelf is $₹ 1200$. To determine the number of tables and bookshelves to be produced every week in order to maximize the total profit, formulate the problem as $LPP$.

• A. Maximize $Z = 1000 x + 1200 y$ Subject to
  $8 x + 11 y \ge 450, 2 x + 3 y \le 100, x \ge 0, y \ge 0$
• B. Maximize $Z = 1000\, x + 1200\, y$ Subject to
  $8 \,x + 11\, y \le 450, 2 \,x + 3 \,y \le 100, x \ge 0, y \ge 0$
• C. Maximize $Z = 1000\, x + 1200\, y$ Subject to
  $8 \,x + 11\, y \le 450, 2 \,x + 3 \,y \ge 100, x \ge 0, y \ge 0$
• D. Maximize $Z = 1000\, x + 1200\, y$ Subject to
  $8 \,x + 11\, y \ge 450, 2 \,x + 3 \,y \ge 100, x \ge 0, y \ge 0$

Answer 1

Answer: (B)

Given $x$ and $y$ units of tables and bookshelves are produced.
Profit on one table is $₹1000$
$\therefore $ Profit on $x$ tables is $₹ 1000 x$
Profit on one bookshelf is $₹1200$
$\therefore $ Profit on $y$ bookshelves is $₹ 1200 y$
$\therefore $Profit $Z= 1000 x + 1200 y$

$\therefore $ Constraints are $8 x + 11 y\le 450, 2 x + 3 y \le 100, x \ge 0, y \ge 0$
$\therefore $ Given problem can be formulated as
Maximize $Z = 1000 x + 1200 y$ Subject to,
$8 x + 11 y \le 450, 2 x + 3 y\le 100, x \ge 0, y \ge 0 $