QUESTION:-6 A FACTORY MANUFACTURES TWO TYPES OF PPE KITS A AND B. EACH TYPE OF PPE KIT REQUIRES THE USE OF TWO MACHINES,AN AUTOMATIC AND A HAND OPERATED MACHINE. IT TAKES 4 MINUTES OF THE AUTOMATIC MACHINE AND 6 MINUTES ON HAND OPERATED MACHINE TO MANUFACTURE PPE KIT A ,WHILE IT TAKES 6 MINUTES ON AUTOMATIC AND 3 MINUTES ON THE HAND OPERATED MACHINE TO MANUFACTURE PPE KIT B,EACH MACHINE IS AVAILABLE FOR ATMOST 4 HOURS A DAY.THE MANUFACTURE CAN SELL THE PPE KIT A AT A PROFIT OF RUPEES 7 AND PPE KIT B AT A PROFIT OF RUPEES 10. ASSUMING THAT HE CAN SELL ALL THE PPE KIT,HE MANUFACTURES. HOW MANY OF EACH TYPE OF PPE KITS SHOULD THE FACTORY OWNER PRODUCE IN A DAY TO MAXIMISE HIS PROFIT,DETERMINE THE MAXIMUM PROFIT?
Answers
Step-by-step explanation:
Let x be the number of packages of screws A and y be the number of packages of screws B that we can make.
Clearly, x,y≥0.
Total time on machine is 4 hr=240 min
∴ for automatic machine , time = 4x+6y≤240⟹2x+3y≤120
∴ for hand machine, time = 6x+3y≤240⟹2x+y≤80
The shaded region is the feasible region.
The profits on Screw A is Rs. 0.7 and on Screw B is Rs. 1. We need to maximize the profits, i.e. maximize z=0.7x+y, given the above constraints.
Now, at A, z=28
at O, z=0
at E, z=41
at D, z=40
Hence, maximum profit is at point E(30,20).
Answer:
30 PPE kits A and 20 PPE kits B
Maximum Profit = Rs 410
Step-by-step explanation:
Hii Mate ^_^
Let x be the number of packages of screws A and y be the number of packages of screws B that we can make.
Clearly, x,y≥0.
Total time on machine is 4 hr=240 min
∴ for automatic machine , time = 4x+6y≤240⟹2x+3y≤120
∴ for hand machine, time = 6x+3y≤240⟹2x+y≤80
The shaded region is the feasible region.
The profits on Screw A is Rs. 0.7 and on Screw B is Rs. 1. We need to maximize the profits, i.e. maximize z=0.7x+y, given the above constraints.
Now, at A, z=28
at O, z=0
at E, z=41
at D, z=40
Hence, maximum profit is at point E(30,20).
Hence,
30 of PPE kits A and 20 PPE kits B are required to maximise the profit.
Maximum Profit = 30 x 7 + 20 x 10 = 210 + 200 = Rs 410
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