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
harkovskaia [24]
3 years ago
12

You must design a closed rectangular box of width w, length l and height h, whose volume is 504 cm3. The sides of the box cost 3

cents/cm2 and the top and bottom cost 4 cents/cm2. Find the dimensions of the box that minimize the total cost of the materials used.
Mathematics
1 answer:
Charra [1.4K]3 years ago
6 0

Answer:

Dimensions will be

Length = 7.23 cm

Width = 7.23 cm

Height = 9.64 cm

Step-by-step explanation:

A closed box has length = l cm

width of the box = w cm

height of the box = h cm

Volume of the rectangular box = lwh

504 = lwh

h=\frac{504}{lw}

Sides which involve length and width and height, cost = 3 cents per cm²

Top and bottom of the box costs = 4 cents per cm²

Cost of the sides C_{s}= 3[2(l + w)h] = 6(l + w)h

C_{s}= 3[2(l + w)h]

C_{s}=6(l+w)(\frac{504}{lw} )

Cost of the top and the bottom C_{(t,p)}= 4(2lw) = 8lw

Total cost of the box C = 3024\frac{(l+w)}{lw} + 8lw

                                      = 3024[\frac{1}{l}+\frac{1}{w}] + 8lw

To minimize the cost of the sides

\frac{dC}{dl}=3024(-l^{-2}+0)+8w=0

\frac{3024}{l^{2}}=8w

\frac{378}{l^{2}}=w ---------(1)

\frac{dC}{dw}=3024(-w^{-2})+8l=0

\frac{3024}{w^{2}}=8l

\frac{378}{w^{2}}=l

w^{2}=\frac{378}{l}-------(2)

Now place the value of w from equation (1) to equation (2)

(\frac{378}{l^{2}})^{2}=\frac{378}{l}

\frac{(378)^{2} }{l^{4}}=\frac{378}{l}

l³ = 378

l = ∛378 = 7.23 cm

From equation (2)

w^{2}=\frac{378}{7.23}

w^{2}=52.28

w = 7.23 cm

As lwh = 504 cm³

(7.23)²h = 504

h=\frac{504}{(7.23)^{2}}

h = 9.64 cm                        

You might be interested in
Solve the system of equations using any method.
stiv31 [10]

Answer:

My answer what I came up with is B And B

4 0
3 years ago
an online furniture store sells chairs for $50 each and tables for $300 each. Every day, the store can ship no more than 53 piec
max2010maxim [7]

If 9 chairs were sold,  the store has to sell 11 tables in order to meet the requirements.

7 0
3 years ago
Jamie scored an 85% on a test that had 20 questions on it. How many question did she get right? How many questions did she get w
SSSSS [86.1K]

Answer:10 wrong

Step-by-step explanation:

I am smart

Hope it helps :)

3 0
3 years ago
Which shape shown has only ONE line of symmetry? A) circle B) rectangle C) isosceles trapezoid D) equilateral triangle
Elena L [17]
Triangle is the final answer
6 0
3 years ago
What is the difference between these fractions?<br><br> +3/4−(+7/8)
Ket [755]

Answer:

1/8

Step-by-step explanation:

3/4 is 6/8 and 6/8 - 7/8 is 1/8

4 0
2 years ago
Read 2 more answers
Other questions:
  • Which quadraric equation has roots -2 and 3
    14·1 answer
  • The diameter of a women's basketball is 23.45 centimeters.
    7·2 answers
  • How do I solve 80+(-22 4/15)
    5·1 answer
  • Which type of asymptote, when it occurs, describes the behavior of a graph when x is close to some number?
    5·1 answer
  • f the probability of an event occurring is​ 0, then it is impossible for that event to occur. B. If the probability of an event
    7·1 answer
  • What's the ratio of 60 and 96
    7·1 answer
  • What percent of 285 is 15?<br><br> Round your answer to the nearest tenth of a percent
    9·1 answer
  • PLEASE ANSWER!!!!!!!!!!
    12·2 answers
  • What is the average rate of change for this quadratic function for the interval fr x=2 to x=4?
    9·1 answer
  • PLEASE HELP
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!