Question

A firm makes two types of furniture : chairs and tables. The contribution to profit for each product as calculated by the accounting department is $Rs.20$ per chair and $Rs.30$ per table. Both products are to be processed on three machines $M_1,M_2$ and $M_3$. The time required in hours by each product and total time available in hours per week on each machine are as follows:

Machine	Chair	Table	Available Time
$M_1$	$3$	$3$	$36$
$M_2$	$5$	$2$	$50$
$M_3$	$2$	$6$	$60$

Which manufacturer gained more profit?

• A. $M_1$
• B. $M_2$
• C. $M_3$
• D. None

Answer 1

The correct option is B $M_2$

For $M_1:$

Total chair posible in one week$=36/3=12$

Total table posible in one week$=36/3=12$

Total profit per week$=12\times Rs.20+12\times Rs.30=Rs.600$

For $M_2:$

Total chair posible in one week$=50/5=10$

Total table posible in one week$=50/2=25$

Total profit per week$=10\times Rs.20+25\times Rs.30=Rs.950$

For $M_3:$

Total chair posible in one week$=60/2=30$

Total table posible in one week$=60/6=10$

Total profit per week$=30\times Rs.20+10\times Rs.30=Rs.900$

Hence, manufacturer used $M_2$ for production to maximize profit.