Does this problem have enough information in it to work it?

[Guest]

If you have $120 to fence a rectangular garden and the fencing for three sides costs $2.00 per foot and for the fourth side $3.00 per foot, what dimensions should you give the gardener to maximize its area?


Does this problem have enough information in it to figure it out? Because I can't. :roll:

 

[stapel]

Draw the rectangle. Pick variables for the length and the width, and label the diagram appropriately.

Edit the "perimeter" formula to give yourself a formula for the cost of the fencing for this (as yet undetermined) length and width.

(Careful: You have two lengths and one width with one cost and one width with another cost. So don't work straight from "P = 2L + 2w". Your first adjustment would need to be something along the lines of "P = 2L + w + w". Then figure in the costs and insert the given total cost for "P".)

Solve this equation for one of the variables. (It doesn't matter which one.)

Now write the area formula, and use the "solving" you just did to replace one of the variables. This will give you an "area" formula with only one variable.

Maximize!

Eliz.