Q. 254.8( 5 Votes )

A cuboidal

Answer :

As base is square so length of base = breadth of base


Let the length and breadth of the base =x


Also, let the height of the godown = y


Let “C” be the total cost of constructing the godown and “V” be the given volume.


As, it is given that, cost is proportional to the area and three times as much cost per square meter is incurred for constructing the roof as compared to the walls.


Area of roof = x2,


area of 4 walls = 4xy


Therefore,


C = k [3x2 + 4xy], … (1)


where k>0 is constant of proportionality


x2y = V … (2)



Substituting value of y from equation (3), in equation (1), we get




On differentiating,



For maximum or minimum value,



So,




When,


Now,



Put, in ,


So,







As, k > 0 so,


Now, as ,


So, C is minimum at


From (3),





So, C is minimum whenand


So,


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