An Optimizing problem

[us3rnotfound]

I'm stumped, please help! 😀

A fence is to be built to enclose a rectangular region of 4800 square feet. The fencing material along three sides costs $3 per foot. The fencing material along the fourth side costs $4 per foot. Find the most economical dimensions of the region.

Edit: I know how to do this kind of problem, but I just need a hint or clue, I don't know the equations to use, except of course for xy = 4800, y = 4800/x.

 

[stan394]

which of the 4 sides are the more expensive one?

ok nevermind

 

[us3rnotfound]

Originally posted by: stan394
which of the 4 sides are the more expensive one?

shouldn't matter.

 

[stan394]

the more expensive side should be on the shorter side of the rectangle.

let's say x > y

C = 3x + 3x + 3y + 4y

and you try to optimize C?

 

[us3rnotfound]

i can take it from here, thx a lot for the equation

 

[PandaBear]

C = 3x + 3x + 3y + 4y = 6x + 7y

xy = 4800

C = 6x + 7(4800/x)

you can do it now, right?

 

[us3rnotfound]

yea

 

[bonkers325]

i forget how to optimize with calculus, but you can do it on excel using the solver function 😛