A business bought three types of computer programs to be used in offices at different locations.
One costs $35 each and uses 190 MB memory, the second costs $50 each and uses 225 MB of memory, and the third costs $60 each and uses 130 MB of memory. If as many of the third type were purchased as the other two combined, with a total cost of $2600 and total memory requirement of 8525 MB, how many of each were purchased

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2014-09-27T02:39:02+05:30

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Number of copies purchased of each program be N1, N2 and N3 respectively.

Total cost in $ =
        35 N1 + 50 N2 + 60 N3 <= 2,600
              7 N1 + 10 N2 + 12 N3 <= 520    -- equation  1
 
 Given  N3 = N1 + N2    --- equation 2
     
               7 N1 + 10 N2 + 12 (N1 + N2) <= 520
               19 N1 + 22 N2 <= 520              --- equation 3

Total memory utilized in MB =
       190 N1 + 225 N2 + 130 N3  >= 8,525 
            38 N1 + 45 N2 + 26 N3  >= 1705  -- equation 4
 
     Substitute for N3 from equation 2
            38 N1 + 45 N2 + 26 (N1+N2)  >= 1705
            64 N1 + 71 N2 >= 1705        -- equation 5

          Solving  equation 3 and equation 5, we get,
             
               N2 (71 - 64*22/19) = 1705 - 64*520/19 ,         N2 = 15
              
          Using equation 3,      19 N1 = 520 - 22*15 ,          N1 = 10
 
          from equation 2, we get         N3 = 25

Checking the memory and costs:

Total cost = 35 N1 + 50 N2 + 60 N3 = $ 350  + 750 + 1500 = $ 2,600
Total memory = 190 N1 + 225 N2 + 130 N3 = 1900 + 3375 + 3250 = 8,525 MB

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