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
sasho [114]
2 years ago
12

Kern Shipping Inc. has a requirement that all packages must be such that the combined length plus the girth (the perimeter of th

e cross section) cannot exceed 99 inches. Your goal is to find the package of maximum volume that can be sent by Kern Shipping. Assume that the base is a square.
a. Write the restriction and objective formulas in terms of x and y. Clearly label each.
b. Use the two formulas from part (a) to write volume as a function of x, V(x). Show all steps.
Mathematics
1 answer:
Ahat [919]2 years ago
4 0

Answer:

Step-by-step explanation:

From the given information:

a)

Assuming the shape of the base is square,

suppose the base of each side = x

Then the perimeter of the base of the square = 4x

Suppose the length of the package from the base = y; &

the height is also = x

Now, the restriction formula can be computed as:

y + 4x ≤ 99

The objective function:

i.e maximize volume V = l × b × h

V = (y)*(x)*(x)

V = x²y

b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):

y + 4x ≤ 99   --- (1)

V = x²y          --- (2)

From equation (1),

y ≤ 99 - 4x

replace the value of y into (2)

V ≤ x² (99-4x)

V ≤ 99x² - 4x³

Maximum value V = 99x² - 4x³

At maxima or minima, the differential of \dfrac{d }{dx}(V)=0

\dfrac{d}{dx}(99x^2-4x^3) =0

⇒ 198x - 12x² = 0

12x \Big({\dfrac{33}{2}-x}}\Big)=0

By solving for x:

x = 0 or x = \dfrac{33}{2}

Again:

V = 99x² - 4x³

\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x

At x = \dfrac{33}{2}

\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})

\implies 198 - 12 \times 33

= -198

Thus, at maximum value;

\dfrac{d^2V}{dx^2}\le 0

Recall y = 99 - 4x

when at maximum x = \dfrac{33}{2}

y = 99 - 4(\dfrac{33}{2})

y = 33

Finally; the volume V = x² y is;

V = (\dfrac{33}{2})^2 \times 33

V =272.25 \times 33

V = 8984.25 inches³

You might be interested in
The scale factor for the lengths of two similar solids is 3/1.
Maslowich

Answer:

A

Step-by-step explanation:

5 0
3 years ago
Help me do this i will pick brailest if right and it is 45 points!
sweet-ann [11.9K]

Answer:

8/21

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
6.749 round to the nerest tenth​
Lorico [155]

Answer: The answer would be 6.750

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
5pm to 5 am how many hours
slega [8]

Answer:

12 hours

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
A box of candies has 14 pieces in total. If 2 of the pieces are strawberry flavored what is the ratio of the other flavors to th
creativ13 [48]

Answer:

12:2 or 6:1

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • “Mia is finally able to upgrade her cell phone. The one she wants costs $220 but she is able to get it for 60% off. She has a co
    7·1 answer
  • Help i need to submits this quickly
    12·2 answers
  • If you miss the bus, then you will be late to school.
    9·2 answers
  • What is the length of this line? khan academy - Distance between two points
    12·1 answer
  • Which one is bigger 1/8 or 2/100
    6·2 answers
  • If both figures have the same perimeter what is the value of x?​
    7·1 answer
  • Adriana is excited to go to the used video game store to buy a gaming system later today. The gaming system usually costs x doll
    7·1 answer
  • Find the value of x.<br> 35<br> 21<br> Х<br> X=<br> = [?]<br> Help
    7·1 answer
  • What is the overlap of Data Set 1 and Data Set 2?
    10·1 answer
  • The price of of a mathematical set. was Ugx 2400 a month ago,and now it is Ugx 3000 - Find The percentage increase​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!