# A furniture trader deals in only two items - chairs and tables. He has rupees 50,000 to invest and a space to store at most 35 items. A chair costs him rupees 1,000 and a table costs him rupees 2,000. The trader earns a profit of rupees 150 and rupees 250 on a chair and table, respectively. Formulate the above problem as an LPP to maximise the profit and solve it graphically.

$\\ Let the number of chairs =\mathrm{x} \\ Nunmber of tables =\mathrm{y} \\ Maximize Profit : P=150 x+250 y \\ Acccording to the question \\ x+y \leq 35 \\ 1000 x+2000 y \leq 50000 \\ \Rightarrow x+2 y \leq 50$

$x \geq 0 , y \geq 0$

For maximum value of profit check at corner point

Value of P at  (0, 25)  = Rs 6250

Value of P at  (20, 15)  = Rs 6750 (Max)

Value of P at  (35,, 0)  = Rs 5250

Hence the maximum value of profit P is Rs 6750 at x(Number of chairs) =20 and y (Number of Tables) = 15.

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