# Optimization Mathematics & Economics Math Problem Paper (Math Problem Sample)

formation of optimal control problem, identification of underlying constraints and solving it

source..Problem 1

* Volume= (U+3)m3, where U is the third digit of the student number. In this case the student number is 1839996 and so the third digit is 9.

So, Volume=(9+3)m3=12m3,

The cost breakdown is given by:

* Cost of the base and top is 8 Pounds/m2

* Cost of the front side is (10+Z)Pounds/m2= 16 Pounds/m2 since the last digit of the student number Z=6.

* Cost of other three sides is 5 Pounds/m2

Let the base, width and height of the rectangular box be x, y, and z, respectively.

We have that xyz=12 which implies that z=12xy.

* Cost of base and top =82xy=16xy

* Front area = xz=x12xy=12ym2 and so cost is =1612y=192y

* Other three sizes area =xz+2yx=12y+24/x and so the cost is

=512y+24x=60y+120x

The total cost of the material =16xy+192y+60y+120x=16xy+252y+120x

Using the AM-GM inequality we have that

16xy+252y+120x3≥316xy(252/y)(120/x)

Or

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