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
fiasKO [112]
3 years ago
5

A company plans to manufacture a rectangular bin with a square base, an open top, and a volume of 800 cm3. The cost of the mater

ial for the base is 0.1 cents per square centimeter, and the cost of the material for the sides is 0.5 cents per square centimeter. Determine the dimensions of the bin that will minimize the cost of manufacturing it. What is the minimum cost?
Mathematics
1 answer:
Nesterboy [21]3 years ago
6 0

Answer:

The dimensions of the box is 20 cm by 20 cm by 2 cm.

The minimum cost of manufacturing the box is 120 cents.

Step-by-step explanation:

Given that, the volume of of rectangular is 800 cm³ with a square base, an open top.

Consider the side of the square base is x cm.

Then length = width = x cm.

and the height be h cm.

The volume of the box is = length×width×height

                                          =(x.x.h) cm³

                                          =x²h cm³

Therefore

x²h=800

\Rightarrow h=\frac{800}{x^2}

The area of the base is = x² cm²  [ since the base is square in shape]

The area of the sides = 2 (length×width) height

                                    =2(x+x)h cm²

                                    =2(2x)h cm²

                                    = 4xh   cm²

The cost of the material for the base is 0.1 cents per square and the cost of the material for the the sides is 0.5 cents.

Total cost of material is C(x)=[(x²h×0.1)+ (4xh×0.5)] cents

∴ C(x)=[(x²×0.1)+ (4xh×0.5)]

⇒C(x)=(0.1x²+2xh)

Putting h=\frac{800}{x^2}

C(x)= 0.1 x^2+2x.\frac{800}{x^2}

\Rightarrow C(x)= 0.1 x^2+\frac{1600}{x} .......(1)

Differentiating with respect to x

C'(x)=0.2x-\frac{1600}{x^2}

Again differentiating with respect to x

C''(x)=0.2+\frac{3200}{x^3}

To find the maximum or minimum cost, we set C'(x)=0

\therefore 0.2x-\frac{1600}{x^2}=0

\Rightarrow 0.2x=\frac{1600}{x^2}

\Rightarrow 0.2x^3=1600

\Rightarrow x^3=\frac{1600}{0.2}

\Rightarrow x^3=8000

\Rightarrow x=20

At x=20 ,the value of C(x) >0. Then at x=20 the value of cost will be maximum.

At x=20 ,the value of C(x) <0. Then at x=20 the value of cost will be minimum.

\therefore C''(x)|_{x=20}= 0.2+\frac{3200}{20^3}>0

The cost of manufacturing the box is minimum when x=20 cm.

Then the height h =\frac{800}{20^2}

                              =2 cm.

The dimensions of the box is 20 cm by 20 cm by 2 cm.

Now putting the value of x in (1)

\therefore C(20)= 0.1\times 20^2+\frac{1600}{20}

            =120 cent.

The minimum cost of manufacturing the box is 120 cents.

You might be interested in
Find the first two random numbers (to the fifth digit after the decimal point) using linear congruential generator with a=4, m=1
yulyashka [42]

the first two random numbers are 4,5.using linear congruential generator with a=4, m=11 and b=0 and 23 as the seed

linear congruential  generator

Xn= an-+b Lm

0d s = 25 , b=6, YM 11, 024

Q O o m) 4, Lu) = 4x2%U)

m= 4x4j = 5 y-5

the numbers are 4, 5.

4.O0000 5.000TO

A linear congruence generator is an algorithm that returns a sequence of pseudorandom numbers computed using discontinuous piecewise linear equations. This method is one of the oldest and best-known pseudorandom number generator algorithms.

The linear congruential generator (LCG) is a pseudorandom number generator (PRNG ) is a class of algorithms. Random number generation plays an important role in many applications, from cryptography to Monte Carlo methods.

Learn more about linear congruential here: brainly.com/question/3168048

#SPJ4

7 0
2 years ago
The figure for the other questions
stira [4]
I can't really measure the angles. I can tell you what they look like they'd be. There are three reasons why not. 
1. The paper is slightly bulged where your hand is
2. The circle is slightly distorted by the camera. This  is not that critical. 
3. It is very hard to measure on a computer screen.
There is nothing you could do to make it any better. In fact, given what you had to do, this is a pretty good representation. 

The Three angles -- Question 22
Using the crudest tools you could imagine, I measured the angle where you have written two 90s between the arms as 132°. That angle opens towards the bottom of the page.

The angle that you have called 95 degrees is actually pretty close. I think you read the upper set of numbers on the protractor when you should have been reading the lower set. I make it 89, but I'll bet it is intended to be 90 degrees. 

The third angle on your right is the same as the first one. It comes in at about 132° using my tools again. 

Question 23
I can help you with this. When you are asked to make an equation, you have to use an equal sign somewhere. 

The sum of the three angles should be 360° I'm going to create an error term because I'm almost sure what I measured won't make 360. All circles when you make angles from any point inside them should make angles that add up to 360° when measured with a protractor if the rays of the angles all start from the same point. [If you don't know what a ray is, call it "the arms of the angles"].

So let's create the equation.
Angle1 + angle2 + angle3 + E = 360°
Angle1 = 89° 
Angle2 = 132°
Angle3 = 132°
E is the error that represents the amount away from 360. Your teacher doesn't expect you to get this or to set it into your equation. The main thing you were supposed to do is add up the angles as you tried to do and state what your total was. This is what was expected.
Total = angle1 + angle2 + angle3
Total = 89 + 132 + 132 = 353. My error is 7° too little. So in my equation E = 7°

What to do
Somebody had to mark this with that green felt. You have a teacher. Go to the teacher and ask to be shown how to read the protractor if that person knows. You just need a bit of help. If the teacher cannot tell you, go to someone in your class who knows about that sort of thing and ask them. You're pretty close to getting it.

6 0
3 years ago
Ab and ba name the same ray.<br><br><br> always<br> sometimes<br> never
vekshin1

The <em><u>correct answer</u></em> is:

never

Explanation:

A ray is named using the endpoint first and then another point on the ray. This means that ray AB has endpoint A and point B on the ray; ray BA has endpoint B and point A on the ray. These are not the same ray, as they do not have the same endpoint.

7 0
3 years ago
Read 2 more answers
A bag contains 8 red marbles, 2 blue marbles and 3 green marbles. If two marbles are drawn out of the bag, what is the exact pro
Anarel [89]

Answer:

Step-by-step explanation:

I don't say u must have to mark my ans as brainliest but my frnd if it has really helped u plz don't forget to thank me...

6 0
3 years ago
Hey guys i ave nothing to do so can we have a conversation please
Kruka [31]
Sure I got time uh I’m not good at conversation starting but if you like anime I can talk about that for a long time but if I stop responding I’m probably doing homework
3 0
3 years ago
Other questions:
  • A bookstore costs $90 a day to keep open, and it spends $13 for each book-
    15·1 answer
  • Please solve R-7=1 ?
    11·2 answers
  • What is 0.8x-x? I will give Brainliest to first answer!!
    7·2 answers
  • The figure shows two parallel lines KL and NO cut by the transversals KO and LN:
    15·2 answers
  • Is 22 to 8 and 88 to 48 a proportion
    13·2 answers
  • X=(a+b)/2 solve for a
    12·1 answer
  • SUBSTITUTION METHOD HELP ME LIKE I NEED IT RN
    11·1 answer
  • Out of the 83 peices of candy in the bag, Fred couldn't eat 15 of them. What percent of candy could Fred not eat? (Round to the
    6·1 answer
  • Andrea wants to pay off her student loan within the next three years, so she has
    10·1 answer
  • The Greatest Common Factor (GCF) of 24, 36, and 48 is O A. 2 O B. 24 O C. 12 O D. 6​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!