# Weird optimization question

1. May 23, 2010

1. The problem statement, all variables and given/known data

Two related type of questions:

1) A rectangular prismic net enclosure for practising golf shots is open at one end. Find the dimensions that will minimize the amount of netting needed and give a volume of 144 m3. Netting is only required on the sides, top, and the far end. Height is x, width is also x, and length is y.

2) A rectangular piece of land is to be fenced using two kinds of fencing. Two opposite sides will be fenced using $6/m fencing, while the other two sided will require$9/m fencing. What are the dimensions of the rectangular lot of greatest area that can be fenced for a cost of $9000? 2. Relevant equations A'(x) = 0 for max/min 3. The attempt at a solution In both questions, I don't know what to do with the 144m3 or the$9000.

What equations am I supposed to use? I could also use tips on how to make equations for these types of questions.

2. May 23, 2010

### hgfalling

Tips:

When doing maximization or minimization problems, you will want to write down the quantity to be minimized or maximized as a function, like f(x,...) = <whatever>. Then you will want to use the other facts in the problem to help simplify the expression for f(x,...) until it is an expression in just one independent variable (often called x, although it can really be anything). Then you take the derivative of the function, set it to zero, and do the usual exploration of the endpoints of the interval and the critical points.

So in the net problem, what is supposed to be maximized or minimized? Can you write down an expression for it in terms of the variables in the problem?

Once you've done that, how many variables are there that f depends on? Can you write another equation involving facts from the problem and two of the variables that f depends on in order to eliminate one of them from the f expression? Then you can do your usual calculus stuff and find the answer.

3. May 23, 2010

### Lancelot59

I find drawing a diagram helps too.

4. May 23, 2010