Question level, secondary

I am a student asking the question

I have no clue how to do this problem. Here is what the professor gave to us:

A=LW

C=E(2L+2W) + I(PL)

Where P = # of partitions

E= cost of exterior of fence

I = cost of interior of fence

C = total cost of fence

This is the picture of how the fence is supposed to look.


We need to derive a formula and express the area in terms of W and have the fence at a maximum area

Mike

Hi Mike,

From the way you describe the problem I am going to assume that the total cost of the fence C is known, as well as P, E and I. What you don't know are the dimensions of the field, L and W.

When you are told to express "A in terms of W", what is expected is an expression for A contains only W and the known quantities C, P, E and I. You have A = LW and hence you need to eliminate L from this expression.

Solve the equation

C=E(2L+2W) + I(PL)
for L and substitute the expression you get into

A = WL
to get an expression for A that contains no L. I got

Finally find the value of W that maximizes A.

Cheers,
Harley
Go to Math Central