Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • A factory manufactures two types of screws A and B, each type requiring the use of two machines, an automatic and a hand-operated. It takes 4 minutes on the automatic and 6 minutes on the hand-operated machines to manufacture a packet of screws ‘

A factory manufactures two types of screws A and B, each type requiring the use of two machines, an automatic and a hand-operated. It takes 4 minutes on the automatic and 6 minutes on the hand-operated machines to manufacture a packet of screws ‘A’ while it takes 6 minutes on the automatic and 3 minutes on the hand-operated machine to manufacture a packet of screws ‘B’. Each machine is available for at most 4 hours on any day. The manufacturer can sell a packet of screws ‘A’ at a profit of 70 paise and screws ‘B’ at a profit of Rs 1. Assuming that he can sell all the screws he manufactures, how many packets of each type should the factory owner produce in a day in order to maximize his profit ? Formulate the above LPP and solve it graphically and find the maximum profit.

 

 

 

 
 
 
 
 

Answers (1)

let the no.of packets of screw 'A' manufactured in a day be x and that of screw B be y
Therefore x\geq 0,y\geq 0

Item Numbers Machine A Machine B Profit
Screw A x 4 minutes 6 minutes Rs 0.7

Screw B

 y 6 minutes 3 minutes Rs 1
Max time
available		   4hrs = 240 min 4hrs-240 min
 

Thus , the constrauals are
4x+by\leq 240\: \: or\: \: 2x+By\leq 120
6x+3y\leq 240\: \: or\: \: 2x+y\leq 80 and Total profit
z= 0\cdot 7x+y
so our LPP will be
Max z= 0\cdot 7x+y
subject to the consrauals
2x+By\leq 120
2x+y\leq 80
and x,y \geq 0
Now, 2x+By\leq 120\; \; and\: \: 2x+y\leq 80

x 0 60
y 40 0

 

x 0 40
y 80 0

 ploting points an graph, we get the fearible region OABC as shown

Corner points Value of Z= 0\cdot 7x+y
C(0,40) 0\cdot 7\left ( 0 \right )+40= 40
B(30,20) 0\cdot 7\left ( 30 \right )+20= 41 \rightarrow Maximum
A(40,0) 0\cdot 7\left ( 40 \right )+0= 28
O(0,0) 0\cdot 7\left ( 0 \right )+0= 0

Hence profit will be maximum if comparing produces 30 packets of screw A and 20 packets of screw B and maximum profit is  41 rupees.
                                                 

Posted by

Ravindra Pindel

View full answer

Similar Questions

Latest Question