1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
olga_2 [115]
3 years ago
14

A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed along the river, the fence on t

he side opposite the river costs $20 per foot, and the fence on the other sides costs $5 per foot. If the field must contain 80,000 square feet, what dimensions will minimize costs?
a) Side Parallel to the River___________ft
b) Each of the other sides _____________ft
Mathematics
1 answer:
Andreas93 [3]3 years ago
4 0

Answer:

a) Side Parallel to the river: 200 ft

b) Each of the other sides: 400 ft

Step-by-step explanation:

Let L represent side parallel to the river and W represent width of fence.

The required fencing (F) would be F=L+2W.

We have been given that field must contain 80,000 square feet. This means area of field must be equal to 80,000.

LW=80,000...(1)

We are told that the fence on the side opposite the river costs $20 per foot, and the fence on the other sides costs $5 per foot, so total cost (C) of fencing would be C=20L+5(2W)\Rightarrow 20L+10W.

From equation (1), we will get:

L=\frac{80,000}{W}

Upon substituting this value in cost equation, we will get:

C=20(\frac{80,000}{W})+10W

C=\frac{1600,000}{W}+10W

C=1600,000W^{-1}+10W

To minimize the cost, we need to find critical points of the the derivative of cost function as:

C'=-1600,000W^{-2}+10

-1600,000W^{-2}+10=0

-1600,000W^{-2}=-10

-\frac{1600,000}{W^2}=-10

-10W^2=-1,600,000

W^2=160,000

\sqrt{W^2}=\pm\sqrt{160,000}  

W=\pm 400

Since width cannot be negative, therefore, the width of the fencing would be 400 feet.

Now, we will find the 2nd derivative as:

C''=-2(-1600,000)W^{-3}

C''=3200,000W^{-3}

C''=\frac{3200,000}{W^3}

Now, we will substitute W=400 in 2nd derivative as:

C''(400)=\frac{3200,000}{400^3}=\frac{3200,000}{64000000}=0.05

Since 2nd derivative is positive at W=400, therefore, width of 400 ft of the fencing will minimize the cost.

Upon substituting W=400 in L=\frac{80,000}{W}, we will get:

L=\frac{80,000}{400}\\\\L=200

Therefore, the side parallel to the river will be 200 feet.

You might be interested in
Heavy rain in Oxford caused the Brandywine Creek to rise. The creek rose three inches the first day, and each day twice as much
alex41 [277]

Answer:

48

Step-by-step explanation:

used a calculator

3 0
3 years ago
Find the EXACT distance between the two points.<br><br><br><br> (4,7) and (−4,9)
bazaltina [42]

ANSWER: y=-\frac{3}{4} x +6 3x=24-4y

Ok done. Thank to me :>

6 0
2 years ago
At the city Museum child admission is $6.40 in adult admission is $9.70 on Sunday 149 tickets were sold for a total sales of $11
Law Incorporation [45]

Answer:

Adult=58

Step-by-step explanation:

c=child, a=adult

6.4c+9.7a=1145 equation 1

c+a=149 equation 2

a=149-c modified equation 2 to isolate a

6.4c+9.7(149-c)=1145 substitute value of a from equation 1 into equation 2

6.4c+1445.3-9.7c=1145

-3.3c=-300.3

c=91

solve for a

c+a=149

91+a=149

a=58

Check answer:

6.4c+9.7a=1145

6.4(91)+9.7(58)=1145

582.40+562.60=1145

1145=1145

8 0
3 years ago
Solve the equation :<br>-3 • ( 2 - x ) + 4 = 2 • ( 1 - 2x) + 3<br>thanks :) ​
kakasveta [241]

Isolate the variable by dividing each side by factors that don't contain the variable.

x  =  1

-6+3x+4=2-4x+3

-8+7x+1=0

7x=7

x=1

4 0
2 years ago
A turtle swims 15 kilometers in 9 hours. How far does the turtle swim in 24 hours?
Pavlova-9 [17]

Answer:

about 40 kilometers

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • Andrea bought 10 bagels and 6 muffins at the bakery. of these items 2/3 of the bagels were multigrain and 3/5 of the muffins wer
    7·1 answer
  • Pete is conducting a survey to determine his customers overall satisfaction about the quality of his company's products. He send
    13·2 answers
  • A florist has 8 roses and 24daffodils. She wants to make as many identical bouquets as possible, with the same combination of ro
    14·1 answer
  • What is the unit rate of 5 packs of gum for 1$?
    9·1 answer
  • The two cones below are similar what is the value of x?
    6·1 answer
  • Identify the base of the parallelogram, given that A=81x2 cm2.
    11·2 answers
  • In triangle KLM, if K is congruent to L, KL = 9x - 40, LM = 7x - 37, &amp; KM = 3x + 23, find x &amp; the measure of each angle.
    6·1 answer
  • If triangle fgh m f = m h, gf = x + 40, hf =3x - 20, and gh = 2x + 20. The length of GH is
    6·2 answers
  • A factory puts 2,000 picture frames in each shipment. How many picture frames will the
    13·1 answer
  • Plz i have no clue and this is due in 15 mins
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!