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A factory makes tennis rackets and cricket bats. A tennis rackets takes 1.5 hour of machine time and 3 hours of craftman's time in its making while a cricket bat takes 3 hour of machine time and 1 hour of cratman's time. In a daythe factory has the availability of not more than 42 hours of machine time and 24 hours of craftman's time. (i) What number of rackets and bats must be made if the factory is to work at full capacity? (ii) If profit on a racket and on a bat is Rs. 20 and Rs. 10 respectively, find the maximum profit of the factory when it works at full capacity. |
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Answer» Solution :Let `x` tennis rackets and `y` cricket bats be made in a day. Now, maximise `z=20x+10y` and constraints `XGE0` `yge0` `1.5x+3yle42` `impliesx+2yle28` `3x+yle24` Now, draw the graph of the straight lines `x=0, y=0, x+2y=28` and `3x+y=24`. Find the FEASIBLE region from the costraints `xge0, yge0, x+2yle28` and `3x+yle24` and shade this feasible region. The vertices of this shaded region are `A(8,0), B(4,12), C(0,14)` and `O(0,0)`. We fnd the value of `Z` at these vertices. Therefore the maixmum PROFIT in RS. 200 when4 tennis racket and 12 cricket bats are made in one day. |
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