# (Solved): PREVIOUS ANSWERS Solve the problems below that pertain to constructing a fence. (a) A farmer wishes ...

PREVIOUS ANSWERS Solve the problems below that pertain to constructing a fence. (a) A farmer wishes to enclose

`8,836ft^(2)`

of land along a river by three sides of fence (the river forms the fourth side of the rectangular area). Find the dimensions which require the minim length of fence. (Let

`x`

be the length of the sides perpendicular to the river, and

`y`

the length of the parallel side.) (b) How does the answer from part (a) change if the fence is divided into three equal sections by two additional lengths of fence parallel to the river. (c) Suppose that, in the situation from part (b), the farmer is not limited by the area of the fence; but instead has only 980 feet of fence available. What is the largest area he can enciose?

`ft^(2)`

Recall that an optimization problem can be solved in three basic steps. Identify the quantity

`Q`

to be minimized or maximized. Use laws of a specific discipline and the given constraints to express

`Q`

as a function of one variable,

`Q=f(x)`

. Then find extreme values of

`Q`

on its domain and solve the mathematical problem. In each case, sketch a picture that describes the given situation. Label the picture with the variables as described. Then write the quantity to be optimized as a function of both

`x`

and

`y`

. How can the fixed area or length of fence be used to write each function as a quantity of only one variable? What is the domain of each function? What are the critical points of each function? What is the absolute maximum or absolute minimum in each case? How can the first derivative test for absolute extreme values be used to determine if there is an absolute maximum or minimum at each critical point of the function describing length of fence? Submit Answer

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