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
Anon25 [30]
3 years ago
14

In order to package one of their products, Acme Box Co. needs to construct a box whose bottom side has length 3 times its width.

The material used to build the top and bottom of the box cost $10 per square foot, while the material used to build the four sides of the box cost $6 per square foot. The box must have a volume of 50 cubic feet. (a) In terms of the length ` of the bottom, the width w of the bottom and the height h of the box (all measured in feet), write a formula for the cost C (in dollars) to construct a box of length `, width w and height h. (b) Given the other conditions specified in the problem, express C as a function of a single variable. (c) Determine the dimensions of the box that minimize the cost. Be sure to justify that you have found dimensions that produce the minimum cost. (You’ll be fired if you submit the maximum cost to your boss!) To the nearest dollar, how much will it cost to build the box at these dimensions?
Business
1 answer:
Len [333]3 years ago
7 0

Answer:

(a)Total Cost, C=20LW+12LH+12WH

(b)C(W)=\dfrac{60W^3+800}{W}

(c)W=1.88ft, L=5.64 ft and H=4.72 ft.

Minimum \:cost, C\approx \$638 $  (to the nearest dollar)$

Explanation:

Given the dimensions of the box to be L,W and H.

(a)

  • The material for the top and bottom of the box cost $10 per square foot
  • The material used to build the four sides of the box cost $6 per square foot.
  • Area of Top and Bottom=2LW
  • Cost of Top and bottom=$10 X 2LW=20LW
  • Area of four Sides =2(LH+WH)
  • Cost of Four Sides =$6*2(LH+WH)=12(LH+WH)
  • Total Cost, C=20LW+12LH+12WH

(b)The bottom side has length 3 times its width.

L=3W

Volume of the box=50 cubic feet.

Volume,V=LWH=3W^2H

3W^2H=50\\H=\dfrac{50}{3W^2}

Substituting L=3W and H=\dfrac{50}{3W^2} into the cost function C.

C=20LW+12LH+12WH

C=20LW+12LH+12WH\\=20*3W*W+12*3W*\dfrac{50}{3W^2}+12W*\dfrac{50}{3W^2}\\=60W^2+\dfrac{600}{W}+\dfrac{200}{W}\\=\dfrac{60W^3+600+200}{W}\\C(W)=\dfrac{60W^3+800}{W}

(c)The minimum cost occurs at the point where the derivative of the cost function equals zero.

If\:C(W)=\dfrac{60W^3+800}{W}\\C'(W)=\dfrac{120W^3-800}{W^2}=0\\120W^3-800=0\\120W^3=800\\W^3=\frac{800}{120}\\ W=1.88

Recall:

L=3W=5.64 feet\\H=\dfrac{50}{3W^2}=\dfrac{50}{3(1.88)^2}=4.72 ft

The dimensions of the box that minimize the cost are W=1.88ft, L=5.64 ft and H=4.72 ft.

Cost of the box at these dimension

C(W)=\dfrac{60W^3+800}{W}\\C(1.88)=\dfrac{60(1.88)^3+800}{1.88}\approx \$638 $  (to the nearest dollar)$

You might be interested in
What is the largest source of revenue in california?
MArishka [77]
The three largest sources of revenue are personal income taxes, sales and use taxes, and corporate income taxes (in that order).
8 0
3 years ago
Kray Inc., which produces a single product, has provided the following data for its most recent month of operations: Number of u
Allushta [10]

Answer:

The variable costing unit product cost was <u>$69.</u>

Explanation:

Variable Product Costing is a situation whereby only the variable costs of production is taking into account to estimating the cost per unit of a product. This implies that none of the fixed cost will be included in the cost of the product.

Based on the explanation above, the variable costing unit product cost to produce a single product by Kray Inc. can be calculated as follows:

Kray Inc.

Calculation of Variable Costing Unit Product Cost

<u>Particulars                                                          Amount ($)     </u>

Direct materials                                                        40

Direct labor                                                               19

Variable manufacturing overhead                           8

Variable selling and administrative expense     <u>     2      </u>

Variable cost per unit                                          <u>     69     </u>

Therefore, the variable costing unit product cost was <u>$69.</u>

5 0
3 years ago
Why net profit will be higher if increases average prices to customers?​
vampirchik [111]

Answer:

Higher prices with same sales quantity will mean greater profit.

Explanation:

Let's hold some variables constant. If a business sells books, and they take the prices up, if they sell the same quantity (at higher prices) this would increase revenues. Higher revenues, less the same cost structure (variable and fixed costs) will lead to a greater profit generation. Of course in the real world, price elasticity of demand comes in play when prices are changed. If prices go up, typically sales quantity will decrease and there may be a net effect in revenue and hence profit. In the simple case where prices go up and sales quantity is unaffected, net profit will rise.

6 0
3 years ago
The business sectors identified in QUESTION 1.3.1
emmainna [20.7K]

Explanation:

poor network , poor electircity

4 0
3 years ago
Design a study that has a false correlation caused by a lurking variable.
Artemon [7]

An example of a study that has a false correlation caused by a lurking variable is " research scientist examines the influence of diet and exercise on a an individual's blood pressure."

<h3>What is a lurking variable in a study?</h3>

Lurking variable is known to be a kind of a  variable that is said not be the explanatory variable nor can it be called the response variable but it is one that is seen to have a relationship (e.g. correlation) with the response and that of the  explanatory variable.

Note that A lurking variable is one that can be falsely identify as a strong relationship that exist between variables or it is one that often hide the true relationship.

Hence, An example of a study that has a false correlation caused by a lurking variable is " research scientist examines the influence of diet and exercise on a an individual's blood pressure."

Learn more about lurking variable  from

brainly.com/question/13285819

#SPJ1

4 0
11 months ago
Other questions:
  • The strength or weakness of the potential entry of rivals as a competitive force is
    5·2 answers
  • Bob and Sally are married, file a joint tax return, report AGI of $120,000, and have two children. Del is beginning her freshman
    11·1 answer
  • You just heard that a​ well-known manufacturer in a different industry segment is going to enter your market with a product that
    5·1 answer
  • Permian Underground Machines &amp; Pipes Co. (PUMP) is in the oil and gas equipment and services industry. It is considering a n
    15·1 answer
  • An audit plan of substantive procedures for cash would not includeA. request a cutoff bank statement be mailed to the client. B.
    12·1 answer
  • A perfectly competitive firm_______.A. Chooses its price to maximize profits.B. Sets its price to undercut other firms selling s
    10·1 answer
  • 1. In what way do organization charts create a picture of an<br> organization?
    13·1 answer
  • How does supply and demand factor into ticket prices
    8·1 answer
  • Which factors are considered when deciding how to make goods and services?
    10·1 answer
  • What are the major causes of the contemporary plight of ldcs in international trade
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!