There are $400 available to fence in a rectangular garden. The fencing for the side of the garden facing the road costs $15 perfoot, and the fencing for the other three sides costs $5 per foot. Consider the problem of finding the dimensions of the largest possible garden.(a) what would be the objective equation and what would be the constraint equations?(b) Express the quantity to be maximized as a function of x.(c) Find the optimal values of x and y.

The answer to this question can be described as follows:

Step-by-step explanation:

A)

The goal is to increase the area and therefore  

Target formula: A = xy  

The limited amount of money, which we have for the fence, and it only has $400  

The equation of constraints: 400=(fence costs parallel to roads) +( 3 other side cost)    

B)

To solve y we use the limiting equation:  

Now, put the value in the y and maximise as much as possible into our goal equation:  

A function for:  

C)

Select the critical value the A(x):  

We now need, with the second derivative, to ensure that this value is maximum:  

not only is there a relative maximum at x = 10, but we can conclude that the

maximum occurs as for all x. We also need y:

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