Question

A small firm makes necklaces and bracelets. The combined number of necklaces and bracelets that it can handle per day is at most $24$. A bracelet takes one hour to make and necklace takes $30$ minutes. The maximum number of hours available per day is $16$. If the profit on a bracelet is Rs. $300$/- and on a necklace is Rs. $100$/-, How many necklaces and bracelets must be made per day to get the maximum profit? Make it as an LLP and solve graphically.

Answer 1

Suppose a number of necklaces manufacture be $x$ and the number of bracelets be $y$.

Since total number of items area at most $24$

$x+y\le \mathrm{24.....}\left(1\right)$

Bracelets takes $1$ hour to manufacture and necklaces take half an hour to manufacture. $x$ items takes $x$ hours to manufacture and if items take $y/2$ hour to manufacture and minimum time available is $16$ hours

$\therefore$ $x/2+y\le \mathrm{16.....}\left(2\right)$

The profit one necklace is Rs. $100$ and the profit one bracelet is Rs. $300$

Let the profit be $t$. Now we wish to maximise the profits so

$max$ $z=100x+300y....\left(3\right)$

So, $x+y\le 24$

$\frac{x}{2}+y\le 16$

max $z=100x+300y$ is required LLP