Construction Cost Problem: rect. w/ most economical fence

[ag.]

Problem: A fence is to be built to enclose a rectangular area of 800 square feet. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Find the dimensions of the rectangle that will allow the most economical fence to be built.

What I Have So Far:

xy = 800
y = 800/x

6(2x + 800/x) + 18 (800/x) or 6(x + 2(800/x)) + 18x

I don't know how to determine which side is the fourth side...

Please help me out. Thanks!

 

[Deleted member 4993]

Re: Construction Cost Problem

Problem: A fence is to be built to enclose a rectangular area of 800 square feet. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Find the dimensions of the rectangle that will allow the most economical fence to be built.

What I Have So Far:

xy = 800
y = 800/x

6(2x + 800/x) + 18 (800/x) or 6(x + 2(800/x)) + 18x

I don't know how to determine which side is the fourth side...

Please help me out. Thanks!

It shouldn't matter. But to start with let's assume x < y then of course

Cost = 6[x + 2(800/x)] + 18x

Optimizing this function, will give you two values of x - and two values of y respectively. Then with the condition x<y - you'll get the correct value.

Assuming x>y, will give you again two sets of solution. Then with x<y condition will find that you'll converge to the same solution as above (now x & y interchanged).