Optimization

[nikchic5]

Okay here is the question....

A farmer with 790 ft of fencing wants to enclose a rectangular area and then divide it into pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?


Thanks so much to anyone who can help me with this problem!! Thanks!

 

[stapel]

Draw the lines of fencing.

Label the drawing, using variables such as "L" and "w" for the length and width of the total area.

Note the relationship between L, w, the pens, and the total length of fencing available. Create an equation to reflect this relationship.

Solve the equation for one of the variables.

Use the two variables to create an equation for the total area. Use the expression from the previous step to substitute for that variable.

You now have an equation for the area in terms of only one of the variables. Maximize.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.