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A leather factory produces two kinds of bags, standard and deluxe. The profit margin is Rs. $20$ on a standard bag and Rs. $30$ on a deluxe bag. Every bag must be processed on a machine A and on machine B. The processing times per bag on the two machines are as follows:

  Time required (Hours/bag)
  Machine A Machine B
Standard bag 4 6
Deluxe bag 5 10

The total time available on machine A is $700$ hours and on machine B is $1250$ hours . Among the following production plans which one meets machine availability constrains and maximizes the profit?

  1. Standard $75$ bags, Deluxe $80$ bags
  2. Standard $100$ bags, Deluxe $60$ bags
  3. Standard $50$ bags, Deluxe $100$ bags
  4. Standard $60$ bags, Deluxe $90$ bags
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