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CBSE Class 12-science Answered

A manufacturer makes Rs 600 profit on stereo system and Rs 400 profit on small tape recorder. A stereo requires 1 hour on machine A, 1 hour on machine B and 4 hours on machine C. A tape recorder requires 2 hours on A, 1 hour on B and 1 hour on C. In a given day, machines A, B and C can working a maximum of 16, 9 and 24 hours respectively. How many stereo systems and tape recorders should be produced per day to maximize the profit.
Asked by Topperlearning User | 01 Sep, 2014, 02:46: PM
answered-by-expert Expert Answer

Let x units of stereos and y units of tape recorders are produced we have following LPP
          Maximum z = 600x + 400y
          st x + 2y  16
          x + y  9
          4x + y  24
          x  0, y  0
         

Corner Points

z = 600x + 40y

0(0, 0)
A(6, 0)
B(5, 4)
C(2, 7)
D(0, 8)

z = 0
z = 3600
z = 4600
z = 4000
z = 3200

Maximum profit is Rs 4600 when 5 stereo system and 4 tape recorders are produced in a day.

Answered by | 01 Sep, 2014, 04:46: PM

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