On a hot summer day we want to cool our room by opening the refrigerator door annd closing all the windows and doors. Will the process work ?

Spring fitted doors close by themselves when released. You want to keep the door open for a long time, say for an hour. If you put a half kg stone in front of the open door, it does not help. The sotne slides with the door and the door gets closed. However, if you sandwitch a 20 g of wood in the small gap between the door and the floor, the door stays open. Explain why a much lighter peice of wood is able to keep the door open while the heavy fails.

Show that the internal energy of the air (treated as an ideal gas) contained in a room remains constant as the temperature changes between day and night. Assume that the atmospheric pressure around remains constant and the air in the room maintains this pressure by communicating with the surrounding through the windows, doors, etc.

A company manufactures two proudcts. A and B on which the profits erarned per unit areRs. 30 and Rs. 40 respectively. Each product is procced on two machines M_(1) and M_(2) . One unit of product A requires on hour of processing time on M_(1) and 2 hours on M_(2) While one unit of product B requires one hour each on M_(1) and M_(2) . Machines M_(1) and M_(2) are availabe atmost 10 hours and 12 hours respectivrely during working day. The company wants to know how many units of proudcts A and B should be produced to maximise the profit. to formulate a linearprogramming problem (i) Write the objective function. (ii) Write all contraints.