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SVEN [57.7K]
4 years ago
14

The base of a rectangular box is to be twice as long as it is wide. The volume of the box is 108 cubic inches. The material for

the top costs $0.50 per square inch and the material for the sides and bottom costs $0.25 per square inch. Find the dimensions that will make the cost a minimum.
Business
1 answer:
goldfiish [28.3K]4 years ago
3 0

Answer:

Explanation:

First we express teh other sides as expression of b (wide)

being the volume: a x b x c

and the base: a x b

if the base is long as wide then:

a = 2b

so we can construct:

2b x b x c = 2b^2 x c = 108

and we clear c:

c = 108/ (2b^2) = 54/b^2

<u>Now we construct the cost formula:</u>

ab x 0.50 (cost for the top part)

now the cost of the sides (there are four) and the bottom part:

(2bc + 2ac + ab) x 0.25

total cost: ab x 0.50 + (2bc + 2ac + ab) x 0.25

we replace a and c as expression of b:

(2b)b \times 0.50 + (2b\frac{54}{b^2} + 2(2b)\frac{54}{b^2} + (2b)b) \times 0.25

and now we solve for b:

b^2 + (\frac{108}{b} + \frac{216}{b} + 2b^2) \times 0.25

b^2 + \frac{81}{b} + \frac{b^2}{2}

(1.5)b^2 + \frac{81}{b}

<u>Now we derivate the cost function: </u> (considering)

a^{x}  = xa\\\frac{1}{a^{x}} = -\frac{1x}{a^{x+1}}

<u />

3b - 81/b^2 = 0

3b^3 = 81

b^3 = 81/3 = 27

b = third root of 27 = 3

<u>now we solve for a: </u>

a = 2b = 2(3) = 6

<u>and last for c:</u>

54/b^2 = 54/(3)^2 = 54/9 = 6

<u>we check if we match the cubic inches:</u>

a x b x c = 108

6 x 3 x 6 = 108

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Answer:

The depreciation expense for year 2 is $13,469

Explanation:

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Computing the depreciation expense for year 2 is as:

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Financial markets a. facilitate the flow of funds from surplus to deficit units. b. facilitate the flow of funds from deficit to
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4 years ago
Calla Company produces skateboards that sell for $68 per unit. The company currently has the capacity to produce 95,000 skateboa
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Answer:

since the special order does not affect current normal sales, its analysis should only consider incremental expenses, not regular expenses:

A) Income statement without the special order

total revenue = $68 x 80,100 = $5,446,800

- COGS                                     = ($2,446,880)

  • Direct materials $897,120
  • Direct labor $608,760
  • Overhead $941,000            

gross profit                               = $2,999,920

- SG&A                                      = ($1,022,000)

  • Selling exp. $559,000
  • Administrative exp. $463,000

net income                               = $1,977,920

B) incremental revenue from special order = 14,900 x $63 = $938,700

incremental costs:

  • direct materials = ($897,120 / 80,100 units) x 17,900 = $200,480
  • direct labor = ($608,760 / 80,100 units) x 17,900 = $136,040
  • overhead = ($658,700 / 80,100 units) x 17,900 = $147,200
  • selling expenses = [($335,400 / 80,100 units) x 17,900] + ($2.70 x 17,900) = $74,952 + $48,330 = $123,282
  • administrative expenses = $940
  • total incremental costs = $607,942

incremental gain from special order = $938,700 - $607,942 = $330,758

Income statement with the special order

total revenue                            = $6,385,500

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  • Direct labor $744,800
  • Overhead $1,088,200            

gross profit                               = $3,454,900

- SG&A                                      = ($1,146,222)

  • Selling exp. $682,282
  • Administrative exp. $463,940

net income                               = $2,308,678

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Answer:

A

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