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jeka57 [31]
2 years ago
12

Consider the following marginal cost function. a. Find the additional cost incurred in dollars when production is increased from

100 units to 150 units. b. Find the additional cost incurred in dollars when production is increased from 500 units to 550 units. C′​(x)=4000−0.4x
Business
1 answer:
weqwewe [10]2 years ago
4 0

Answer:   (a) $197,500

(b) $ 189,500

Explanation:

Given : The marginal cost function : C′​(x)=4000−0.4x

To find the cost function, we need to integrate the above function with respect to x.

Now, the additional cost incurred in dollars when production is increased from 100 units to 150 units will be:-

\int^{150}_{100}\ C'(x)\ dx\\\\=\int^{150}_{100} (4000-0.4x)\ dx\\\\=[4000x-\dfrac{0.4x^2}{2}]^{150}_{100}\\\\=[4000(150)-\dfrac{0.4(150)^2}{2}-4000(100)+\dfrac{0.4(100)^2}{2}]\\\\=[600000-4500-400000+2000]\\\\=197500

Hence, the additional cost incurred in dollars when production is increased from 100 units to 150 units= $197,500

Similarly,  the additional cost incurred in dollars when production is increased from 500 units to 550 units :-

\int^{550}_{500}\ C'(x)\ dx\\\\=\int^{550}_{500} (4000-0.4x)\ dx\\\\=[4000x-\dfrac{0.4x^2}{2}]^{550}_{500}\\\\=[4000(550)-\dfrac{0.4(550)^2}{2}-4000(500)+\dfrac{0.4(500)^2}{2}]\\\\=[2200000-60500-2000000+50000]\\\\=189,500

Hence, the additional cost incurred in dollars when production is increased from 500 units to 550 units = $ 189,500

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const2013 [10]

Question not complete

Direct Labour Cost is missing

Direct Labor Cost ----- $50,000.00 $270,000.00

Answer:

a.

Overhead Rate (Cutting Department) = $5.5 per machine hour = $5.5 per machine hour

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c. Yes

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a. Compute the predetermined overhead rate to be used in each department.

Given

Cutting Department

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Machine Hours = 48,000

Finishing Department

The Finishing Department bases its rate on direct labor-hours.

Manufacturing Overhead Costs = $366,000

Direct Labour Cost = $270,000

Overhead Rate (Cutting Department) = Manufacturing Overhead Cost/Machine Hours

Overhead Rate (Cutting Department) = $264,000/48,000

Overhead Rate (Cutting Department) = $5.5 per machine hour

Overhead Rate (Finishing Department) = Manufacturing Overhead Cost/Machine Hours

Overhead Rate (Finishing Department) = $366,000/$270,000

Overhead Rate (Finishing Department) = 1.36

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b.

The Cutting Department bases its rate on machine-hours

Given

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Overhead Rate = $5.5 per machine hours ------ Calculated

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Given

Direct Labour Cost = 150

Overhead Rate = 136% labour cost ------ Calculated

Overhead Applied (Cutting Department) = 80 * 5.5

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