The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension be?

*Hint: Let x represent one of the dimensions, and then define the other dimensions in terms of x.

Question

The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension be?

*Hint: Let x represent one of the dimensions, and then define the other dimensions in terms of x.

anonymous · Answer

does the "sum of the dimensions" mean base time width times height?  if so then you can write 
$$x+1.5x+y=6$$ or 
$$2.5x+y=6$$ solve that for $y$

haleyelizabeth2017 · Answer

I'm just not sure how to write the equations.....something that has to do with 1.5x + something =6....

haleyelizabeth2017 · Answer

okay that would be y=-2.5x+6

haleyelizabeth2017 · Answer

I'm not sure....what I put is all they gave me :(

anonymous · Answer

then the volume is $$V(x)=x\times 1.5x\times (-2.5x+6)$$

haleyelizabeth2017 · Answer

okay so that is just like what I'm used to! :D

anonymous · Answer

probably easier to use fractions instead of decimals
in any case you can minimize that one using calc

haleyelizabeth2017 · Answer

I like decimals better :P lol idk why........but I am going to do x*1.5x first which is $1.5x^2$ then I multiply that by -2.5x+6.........which would equal $-3.75x^3+9x$ correct?

haleyelizabeth2017 · Answer

how does finding that help to find the dimensions?