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#### rsyed5

##### New member

- Aug 15, 2013

- 5

- Thread starter rsyed5
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- Aug 15, 2013

- 5

As for the length, notice that to the left, exactly half of the total 120cm is wasted, leaving 60cm, and then another x cm is removed from the right. So the length is 60 - x.

This is the correct diagram.The company asks you to generate the dimensions of the

rectangular tank that will maximize its volume.

(a) List any constraints on the length (L), width (W)

and height (H) of the tank.

(b) Determine the dimensions as exact values and also

as approximate values correct to two decimal places.

Code:

```
: - - - - 120 - - - - :
- *-------*---*-------*---* -
: |///////|///| |///| H
: * - - - * - * - - - * - * -
: | | | | | :
80 | | | | | W
: | | | | | :
: * - - - * - * - - - * - * -
: |///////|///| |///| H
- *-------*---*-------*---* -
: - L - : H : - L - : H :
```

. . Hence: .[tex]0 < L < 60[/tex]

Reading down the right side: .[tex]2H + W \:=\:80\;\;[2][/tex]

. . Hence: .[tex]0 < W < 80\,\text{ and }\,0 < H < 40[/tex]

From [1]: .[tex]L \:=\:60-H[/tex]

From [2]: .[tex]W \:=\:80-2H[/tex]

We have: .[tex]V \:=\:LWH[/tex]

Hence: .[tex]V \:=\: (60-H)(80-2H)H[/tex]

And we must maximize: .[tex]V \:=\:2H^3 - 200H^2 + 4800H[/tex]