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
Katena32 [7]
3 years ago
11

I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing

for the north and south sides costs only $2 per foot. I have a budget of $128 for the project. What are the dimensions of the vegetable patch with the largest area I can enclose?
Mathematics
1 answer:
Anestetic [448]3 years ago
5 0
Let the lengths of the east and west sides be x and the lengths of the north and south sides be y.  the dimensions you want are therefore x and y.

The cost of the east and west fencing is $4*2*x; the cost of the north and south fencing is $2*2*y.  We have to put in that "2" because there are 2 sides that run from east to west and 2 sides that run from north to south.



The total cost of all this fencing is $4(2)(x) + $2(2)(y) = $128.  Let's reduce this by dividing all three terms by 4:  2x + y = 32.

Now we are to maximize the area of the vegetable patch, subject to the constraint that 2x + y = 32.  The formula for area is A = L * W.  Solving 2x + y = 32 for y, we get y = -2x + 32.

We can now eliminate y.  The area of the patch is (x)(-2x+32) = A.  We want to maximize A.

If you're in algebra, find the x-coordinate of the vertex of this quadratic equation.  Remember the formula x = -b/(2a)?  Once you have calculated this x, subst. your value into the formula for y:  y= -2x + 32.

Now multiply together your x and y values to obtain the max area of the patch.


If you're in calculus, differentiate A = x(-2x+32) with respect to x and set the derivative equal to zero.  This approach should give you the same x value as before; the corresponding y value will be the same;  y=-2x+32.

Multiply x and y together.  That'll give you the maximum possible area of the garden patch.
You might be interested in
In the fraction 7/8, the numerator denominator is 7.
ololo11 [35]

7/8 is the fraction

7 is the numerator

8 Is the denominator

8 0
3 years ago
Read 2 more answers
Taiwan isnt a country prove me wrong
Kay [80]

Answer:

Taiwan is a country.

Step-by-step explanation:

According to Wikipedia, "Taiwan, officially the Republic of China (ROC), is a country in East Asia. It shares maritime borders with the People's Republic of China (PRC) to the northwest, Japan to the northeast, and the Philippines to the south. The main island of Taiwan, formerly known as Formosa, has an area of 35,808 square kilometres (13,826 sq mi), with mountain ranges dominating the eastern two-thirds and plains in the western third, where its highly urbanised population is concentrated. The capital is Taipei, which, along with New Taipei and Keelung, forms the largest metropolitan area of Taiwan. Other major cities include Kaohsiung, Taichung, Tainan and Taoyuan. With 23.45 million inhabitants, Taiwan is among the most densely populated countries in the world.

That's it, it is all based on research.

7 0
3 years ago
Read 2 more answers
A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in t
Zinaida [17]

Answer:

a) p(x) = 300 - 3

b) P(x) = -3 x² + 285 x

c) Price of per room per day  = $ 157.5

when Number of rooms occupied , x = 47.5

Step-by-step explanation:

Given - A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in the charge per room per day, one more room is vacant. Each occupied room costs an additional $15 per day to maintain.

To find - a) Find the demand function, expressing p, the price charged for each room per day, as a function of x, the number of rooms occupied.

             b) Find the profit function P(x).

             c) Find the price of per room per day the motel should charge in order to maximize its profit.

Proof -

a)

Let

(x, y) be the point

where x represents number of rooms occupied

and y represents price of room per day.

Now,

Given that,

a room is priced at $60 per day, all 80 rooms of the motel are occupied.

So, point becomes (80, 60)

And  given that For every $3 rise in the charge per room per day, one more room is vacant.

So, point becomes (79, 63)

Now, we have two points (80, 60), (79, 63)

Let us assume that,

p(x) be the price charged for each room per day

Now,

By using point - slope formula , we get

p -60 = \frac{(63 - 60}{(79 - 80)} (x - 80)

⇒p -60 = (-3)(x-80)

⇒p-60 = 240 -3 x

⇒p(x) = 240 + 60 -3 x

⇒p(x) = 300 - 3 x

b)

Given that,

Each occupied room costs an additional $15 per day to maintain.

Let C(x) be the cost function,

Then C(x) =15 x

now,

Revenue function,

R(x) =x*p

      = x*(300 -3 x )

      = 300 x - 3 x²

⇒R(x) = 300 x - 3 x²

Now,

We know

Profit function = Revenue function - Cost function

⇒P(x) = R(x)-C(x)

⇒P(x) = (300 x -3 x²) -15 x

⇒P(x) = -3 x² + 285 x

c)

P'(x) = -6 x +285

For Maximize profit , Put P'(x) = 0

⇒-6 x+ 285 =0

⇒6 x= 285

⇒x = \frac{285}{6}

⇒x= 47.5

∴ we get

Maximize profit is when price, p = 300 - 3x

                                                      = 300 -3(47.5)

                                                      = $157.5

⇒Price of per room per day  = $ 157.5

when Number of rooms occupied , x = 47.5

5 0
3 years ago
- What is the range of the following set of points: {(3, 4), (7, - 2), (11, – 8)}?
konstantin123 [22]

Answer:

B) {-8,-2,3,4,7,11}

Step-by-step explanation:

range is y

3 0
3 years ago
Jared has some quarters and dimes that total $5.50. If he has 8 more quarters that dimes, how much dimes does Jared have?
MAXImum [283]
Answer: 10 dimes

Solve using system of equations.
q=number of quarters and d=number of dimes
.25q+.10d=5.50 because the total of dimes and quarters is $5.50
8+d=q because there are 8 more quarters than dimes
substitute 8+d for q into the first equation to get .25(8+d)+.10d=5.50
then simplify
2+.35d=5.50
.35d=3.50
d=10 he has 10 dimes
8 0
3 years ago
Other questions:
  • Please Answer Quick 65 Points ! !
    5·1 answer
  • Carmen bought x candy bars. She gave three of them away.
    13·1 answer
  • How do i do 100-50 3/8
    14·2 answers
  • Solve for the indicated variable. 5y + 4x = 6 for x <br> solve for x<br> x=
    10·1 answer
  • // QuartsToGallons.java public class QuartsToGallons { public static final int QUARTS_IN_GALLON = 4; public static void main(Str
    5·1 answer
  • Write 1.96 ...... as a mixed number in simplest form.
    14·1 answer
  • The following steps show how the right side of 1 – cos(2x) = tan(x)sin(2x) can be rewritten to show it is an identity.
    6·2 answers
  • a 29 foot rope is cut into 2 pieces. the longer feet is two feet longer than twice the shorter piece. how long is each piece? PL
    10·1 answer
  • 8.
    12·1 answer
  • 14. Mashud and Iqbal are security guards at a top secret federal vault. They each work 8 hour shifts, consecutively. If Mashud b
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!