a shopkeeper sells only tables and chairs he has only Rs 6000 to invest and has a space for at most 20 items. A table cost Rs 400 and a chair cost hin Rs 250. He can sell a table at a profit of Rs 40 and chair at a profit of Rs 30. Supposing he can sell whatever he buys formulate the problem as a LPP and solve it graphically for maximum profit?

Dear Student,

Let the shopkeeper purchase x tables and y chairs.So,x0, y0              ....1shopkeeper has a space atmost 20 items. So,x+y20                 ....2Since he can invest only Rs 6000. Therefore,400x+250y60008x+5y120      ....3And, the objective function;p=40x+30y           ....4

From the graph, the feasible area is BCD. Now,The value of P at C0,20=40×0+30×20=600The value of P at D0,24=40×0+30×24=720The value of P at B203,403=40×203+30×403=20003Thus, the maximum gain will be when zero tables and 24 chairs are purchased.

Hope this would have clear your doubt. Do let us know in case of any further concerns.


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