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kogti [31]
2 years ago
14

Departmental information for the four departments at Samoa Industries is provided below. Total Cost Cost Driver Square Feet Numb

er of Employees Janitorial $150,000 Square footage serviced 200 40 Cafeteria 50,000 Number of employees 20,000 12 Cutting 1,125,000 4,000 120 Assembly 1,100,000 16,000 40 The Janitorial and Cafeteria departments are support departments. Samoa uses the sequential method to allocate support department costs, first allocating the costs from the Janitorial Department to the Cafeteria, Cutting, and Assembly departments. Determine the dollar amount of the Janitorial Department costs to be allocated to the:
Business
1 answer:
Pepsi [2]2 years ago
4 0

Question Completion:

(a) Cafeteria, (b) Cutting, and (c) Assembly departments.

Answer:

Samoa Industries

               Departmental   Square      Number        Allocation of

                    Cost               Feet     of employees     Janitorial

Janitorial   $150,000                                               ($150,000)

Cafeteria       50,000         20,000           12                   75,000  

Cutting       1,125,000          4,000         120                   15,000

Assembly 1,100,000          16,000           40                 60,000

Explanation:

a) Data and Calculations:

                                  Total Cost   Cost Driver   Square Feet   Number of

                                                                                                   Employees

Janitorial                    $150,000

                                             Square footage serviced  200           40

Cafeteria                       50,000 Number of employees 20,000     12

Cutting                       1,125,000                                     4,000              120

Assembly                   1,100,000                                    16,000              40

b) Allocation of Janitorial department cost is based on  square footage serviced:

Cafeteria = 20,000/40,000 * $150,000 = $75,000

Cutting = 4,000/40,000 * $150,000 = $15,000

Assembly = 16,000/40,000 * $150,000 = $60,000

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Answer:

(0.5 \times 8q_2)+q_2=100\\\\5q_2=100\\\\q_2=20

since q_2 = 20

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Explanation:

U(q₁ q₂)

q_1^{0.8}q_2^{0.2}\\\\P_1= \$0.5 \ P_2=\$1 \ Y=100

Budget law can be given by

P_1q_1+P_2q_2=Y\\\\0.5q_1+q_2=100

Lagrangian function can be given by

L=q_1^{0.8}q_2^{0.2}+ \lambda (100-0.5q_1-q_2)

First order condition csn be given by

\frac{dL}{dq} =0.8q_1^{-0.2}q_2^{0.2}-0.5 \lambda=0\\\\0.5 \lambda=0.8q_1^{-0.2}q_2^{0.2}---(i)

\frac{dL}{dq} =0.2q_1^{0.8}q_2^{-0.8}- \lambda=0\\\\ \lambda=0.2q_1^{0.8}q_2^{-0.8}---(ii)

\frac{dL}{d \lambda} =100-0.5q_1-q_2=0\\\\0.5q_1+q_2=100---(iii)

From eqn (i) and eqn (ii) we have

\frac{0.5 \lambda}{\lambda} =\frac{0.8q_1^{-0.2}q_2^{0.2}}{0.2q_1^{0.8}q_2^{-0.8}} \\\\0.5=\frac{4q_2}{q_1}\\\\q_1=8q_2}

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(0.5 \times 8q_2)+q_2=100\\\\5q_2=100\\\\q_2=20

since q_2 = 20

q_1 = 8*20\\\\q_1=160

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