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iren2701 [21]
2 years ago
9

The quantity demanded x for a product is inversely proportional to the cube of the price p for p > 1. When the price is $10 p

er unit, the quantity demanded is 64 units. The initial cost is $140 and the cost per unit is $4. What price will yield a maximum profit? (Round your answer to two decimal places.)
$______
Business
1 answer:
Delvig [45]2 years ago
4 0

Answer:

$6.00

Explanation:

Given data

quantity demanded ( x )  ∝ 1 / p^3       for p > 1

when p = $10/unit , x = 64

initial cost = $140, cost per unit = $4

<u>Determine the price that will yield a maximum profit </u>

x = k/p^3 ----- ( 1 ).  when x = 64 , p = $10 , k = constant

64 = k/10^3

k = 64 * ( 10^3 )

  = 64000

back to equation 1

x = 64000 / p^3

∴ p = 40 / ∛x

next calculate the value of revenue generated

Revenue(Rx) = P(price ) * x ( quantity )

               = 40 / ∛x * x   =  40 x^2/3

next calculate Total cost of product

C(x) = 140 + 4x

Maximum Profit  generated = R(x) - C(x) = 0

                                              = 40x^2/3 - 140 + 4x  = 0

                                              =  40(2/3) x^(2/3 -1) - 0 - 4 = 0

                                            ∴ ∛x = 20/3    ∴     x = (20/3 ) ^3 = 296

profit is maximum at x(quantity demanded ) = 296 units

hence the price that will yield a maximum profit

P = 40 / ∛x

  = ( 40 / (20/3) )  = $6

                                             

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pishuonlain [190]

Answer: 6.40%

Explanation:

Use Excel to calculate this by the formula;

= RATE(Nper,Pmt,-Pv,Fv)

Nper is number of periods = 20 * 2 = 40 semi annual periods

Pmt is the payment = $6%/2 * 1,000 = $30

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Fv is future value or face value = $1,000

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= 6.40%

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Under absorption costing, fixed manufacturing overhead is expensed at the time the units are produced. Under variable costing, f
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Answer:

A. True

Explanation:

In the case of absorption costing, the fixed manufacturing overhead should be incurred at the time when the units are generated or produced. While on the other hand, in the case of variable costing the fixed manufacturing overhead should be incurred at the time when the units are sold

Therefore the given statement is true

Hence, the correct option is a.

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Answer:

Part 1.  

Plantwide overhead rate for Laval using direct labor hours as a base. is $1.60 per Direct Labor Hour

Part 2.

Total manufacturing cost per unit for the aluminum desk lamp using the plantwide overhead rate is $78.76

Part 3. Compute departmental overhead rates based on machine hours in the fabricating department and direct labor hours in the assembly department.

                                         Fabricating                  Assembly              

Overheads (R)                      390000                         410000      

Department Cost Driver      152000                         290000      

Overhead Rate                         2.57                                 1.41            

Therefore Overhead Rates are :

            Fabricating Department $ 2.57 per Machine Hour  

            Assembly Department $1.41 per Labor Hour          

Part 4. Use departmental overhead rates from requirement 3 to determine the total manufacturing cost per unit for the aluminum desk lamps.

Direct materials ($270000/21000)                                         12.86

Direct labor:

       Fabricating department(6500/21000×$29)                   8.98

       Assembly department(15200/21000×$26)                   18.82

Overheads:

       Fabricating department(152000/21000×$2.57)           18.60

       Assembly department (290000/21000×$1.41)             19.47

Total manufacturing cost per unit                                         78.73

Explanation:

Part 1.  Plantwide overhead rate for Laval using direct labor hours as a base.

Overhead Rate = Total Overheads/Total Direct Labor Hours

                          = $1.60 per Direct Labor Hour

                                            Fabricating                  Assembly         Total      

Overheads (R)                      390000                         410000       800000

Direct Labor Hrs                  210000                         290000       500000

Overhead Rate                                                                                   1.60

Part 2. Total manufacturing cost per unit for the aluminum desk lamp using the plantwide overhead rate

Direct materials ($270000/21000)                                         12.86

Direct labor:

       Fabricating department(6500/21000×$29)                   8.98

       Assembly department(15200/21000×$26)                   18.82

Overheads:

       Fabricating department(210000/21000×$1.60)            16.00

       Assembly department (290000/21000×$1.60)            22.10

Total manufacturing cost per unit                                         78.76

Part 3. Compute departmental overhead rates based on machine hours in the fabricating department and direct labor hours in the assembly department.

Part 4. Use departmental overhead rates from requirement 3 to determine the total manufacturing cost per unit for the aluminum desk lamps.

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Answer:

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