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
9966 [12]
3 years ago
6

The supreme shipping company can load trucks with both rectangular and cylindrical containers. A rectangular container has a vol

ume of 100 feet and weighs 200 pounds. Hey cylindrical container has a volume of 200 ft.³ cubed and weighs 100 pounds. Each truck has room for at most 4200 ft.³ of containers and can carry a maximum of 4800 pounds. If the shipping company charges $60 to ship a rectangular container and $55 to ship a cylindrical container how many of each should they ship to maximize their income
Mathematics
1 answer:
soldi70 [24.7K]3 years ago
3 0

the number of rectangular containers to maximze their income is 18 while the number of cylindrical containers to maximize income is 12.

The maximum income is $1740

Let x be the number of rectangular containers and y the number of cylindrical containers.

Since a rectangular container has a volume of 100 ft ³and weighs 200 pounds and a cylindrical container has a volume of 200 ft.³ and weighs 100 pounds, and each truck has room for at most 4200 ft.³ of containers and can carry a maximum of 4800 pounds,

We have that the maximum volume of the truck V = 100x + 200y.

Also, the maximum weight of the truck is W = 200x + 100y

Since V = 4200 ft.³  and W = 4800 pounds,

100x + 200y = 4200 and 200x + 100y = 4800

x + 2y = 42 (1) and 2x + y = 48 (2)

Multiplying (1) by 2 and (2) by 1, we have

2x + 4y = 84 (3) and 2x + y = 48 (4)

Subtracting (4) from (3), we have

2x + 4y = 84

-

2x + y = 48

3y = 36

y = 36/3

y = 12

Substituting y into (1), we have

x + 2y = 42

x + 2(12) = 42

x + 24 = 42

x = 42 - 24

x = 18

Also, since the shipping company charges $60 for a rectangular container and $55 for a cylindrical container, the income, P = 60x + 55y

Since x = 18 and y = 12, the maximum income is P = 60x + 55y

= 60(18) + 55(12)  

= 1080 + 660

= $1740

So, the number of rectangular containers to maximze their income is 18 while the number of cylindrical containers to maximize income is 12.

The maximum income is $1740

Learn more about maximum income here:

brainly.com/question/24559594

You might be interested in
What is 4 3/8 - 5 1/2 ? Enter your answer as a fraction in simplest form
maksim [4K]

Answer:

6 1/6

Step-by-step explanation:

5 0
2 years ago
A medium water hose can fill a pool in 30 minutes. A larger water hose can fill the same pool in 20 minutes. If both hoses are t
Sladkaya [172]

t/30 + t/20 = 1

12 minutes

Step-by-step explanation:

just did the instruction on edgenuity

4 0
3 years ago
Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x
djverab [1.8K]

I'll assume the ODE is

y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}

Solve the homogeneous ODE,

y'' - 3y' + 2y = 0

The characteristic equation

r^2 - 3r + 2 = (r - 1) (r - 2) = 0

has roots at r=1 and r=2. Then the characteristic solution is

y = C_1 e^x + C_2 e^{2x}

For nonhomogeneous ODE (1),

y'' - 3y' + 2y = e^x

consider the ansatz particular solution

y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x

Substituting this into (1) gives

a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1

For the nonhomogeneous ODE (2),

y'' - 3y' + 2y = e^{2x}

take the ansatz

y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}

Substitute (2) into the ODE to get

b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1

Lastly, for the nonhomogeneous ODE (3)

y'' - 3y' + 2y = e^{-x}

take the ansatz

y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}

and solve for c.

ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16

Then the general solution to the ODE is

\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}

6 0
1 year ago
What is [3.4(6x+2)+3]+4p-3x? PLS need help
inna [77]
Step 1: simplify

[3.4 ( 6 x + 2 ) +3] + 4 p -3 x 

Pemdas!

 6x+2=8x

3.4+3=6.4

6.4+8x=14.4

14.4x+4p=18.4xp+3= 21.4xpx 

x=8

p=18.4

Other x = 21.4
3 0
3 years ago
What is the area of this quadrilateral?
Sever21 [200]
24 square feet is the answer
7 0
3 years ago
Other questions:
  • ANSWER THE QUESTION IN THE PICTURE?<br><br>(I selected a random answer)
    6·2 answers
  • -3(1 – 3x) + 2x
    14·1 answer
  • 4 times as much as 3 is
    6·2 answers
  • Find the angle measure in degrees
    9·1 answer
  • How would you write a number line for -3-1.5
    13·1 answer
  • What is the solution to the system of linear equations?
    11·1 answer
  • Use the given values to find the missing lengths in the figure. If necessary, express your answer as a
    13·1 answer
  • Plz help me asap wil give brainliest​​
    11·1 answer
  • I would love some help!! 13 points and brainlest to whoever gives a correct answer!
    5·1 answer
  • If (x+3)(x-5)=x^2 +mx-15, the value of m is...?<br> Pls explain the answer, thx!
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!