a shopkeeper sells only tables and chairs he has only Rs 6000 to invest and has a space for at - Maths - Linear Programming

Question

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?

Priyanka Kedia · Accepted Answer

Dear Student,

Let the shopkeeper purchase x tables and y chairs
So,x≥0, y≥0              
1shopkeeper has a space atmost 20 items
 So,x+y≥20                 
2Since he can invest only Rs 6000
 Therefore,400x+250y≤6000⇒8x+5y≤120      
3And, the objective function;p=40x+30y           
4
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_56adb72289f3d%20png"
style="width: 474px; height: 282px;">
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