# How can I determine the maximum and minumum number of students using calculus that can fit in a room given the width and length. Please help me... really need help

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Let us assume length of the room be x and width of the room be y.

Let further assume that room is rectangular.

Define area as a function of x and y i.e.

`A(x,y)=x xx y`

If relation between x and y is known to us then A(x,y) can be transformed into a single variable function either in x or in y.

Now let hythetically assume that average area B(x,y) requred an individual is known in term of lenth and width relation with that dimension of the room.

Define Lagranges function

L(A,B)=A(x,y)+`lambda` B(x,y)

`(delL)/(delx)=0,(delL)/(dely)=0, and (delL)/(del lambda)=0`

Solve for x,y and lambda .Calculate second derivative and apply test when it give max or min.

By this method you can estimate min /max .

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do you have another method? by just using derivatives.