Chapter 4.3, Problem 51AYU

(a)

To determine

To write:a function $C\left(x\right)$ to describe the cost of the project.

Answer to Problem 51AYU

The required function is $C\left(x\right)=16x+\frac{5000}{x}+100$

Explanation of Solution

Given:

Area= 1000 square feet.

Fencing for the sideparallel to the river is $5 per linear foot

Fencing for theother two sides is $8 per linear foot

The four corner postsare $25 apiece.

Calculation:

Consider the function with concentration of a drug at different point of time.

Find the function from the information.

Let the side parallel to the river be $y$

Now as the area is $1000$ that is

  $x.y=1000$

So now

  $16x+5y+100=C\left(x\right)$

Now replacing $ybyx$

  $C\left(x\right)=16x+\frac{5000}{x}+100$

Conclusion:

Therefore, the required function is $C\left(x\right)=16x+\frac{5000}{x}+100$

(b)

To determine

To find:the domain of $C$

Answer to Problem 51AYU

The domain is: $\left(-\infty ,0\right)\cup \left(0,\infty \right)$

Explanation of Solution

Calculation:

The function on all real numbers except zero, that is the function is defined on all real numbers except $x=0$

Then the domain of the function is $x;x\cancel{=}0$

  

The domain is: $\left(-\infty ,0\right)\cup \left(0,\infty \right)$

Conclusion:

The domain is: $\left(-\infty ,0\right)\cup \left(0,\infty \right)$

(c)

To determine

To graph: $C=C\left(x\right)$ by using a graphing utility

Answer to Problem 51AYU

  

Explanation of Solution

Calculation:

  

Conclusion:

Thus, the required graph is drawn.

(d)

To determine

To find:the dimensions of the cheapest enclosure.

Answer to Problem 51AYU

The dimension of the cheapest enclosure is 17.7 ft. to 56.6 ft. long side is parallel to river.

Explanation of Solution

Calculation:

It can be clearly seen from the graph that the dimension of the cheapest enclosure is 17.7 ft. to 56.6 ft. long side is parallel to river.

Conclusion:

Therefore, the dimension of the cheapest enclosure is 17.7 ft. to 56.6 ft. long side is parallel to river.