Question

A manufacturer buys large quantities of certain fuel pumps. He finds that his cost depends on the number of cases, q, bought at the same time according to the table below, where cost(q), measured in dollars, is the total cost of purchasing q cases. Find the marginal cost at q = 108.
9 96 100 104 108 112 116 cost(q)
1780 1850 1920 1990 2060 2120
a) $15.80/case
b) $10.50/case
c) $17.50/case
d) $14.00/case

Answer 1

Answer:

The correct option is c) $17.50/case.

Step-by-step explanation:

Note: The data in the question are merged. The data are therefore sorted and the whole question is represented before answering the question. Please, see the attached pdf file for the sorted data and the represented question.

The explanation of the answer is now given as follows:

Marginal cost refers to the cost incurred in order to produce one more unit of a product.

Therefore, marginal cost is the change in the total cost that is caused by a one-unit increase in the quantity of a commodity that is produced.

From the table in the question, the marginal cost at q = 108 can be calculated as follows:

Change in total quantity at 180 cases = 108 - Number of cases immediately before 108 = 180 - 104 = 4

Change in total cost at 180 cases = Total cost at 108 cases - Total cost immediately before 108 cases = 1990 - 1920 = 70

Marginal cost at 108 cases = Change in total cost at 180 cases / Change in total quantity at 180 cases = 70 / 4 = 17.50 per case

Therefore, the correct option is c) $17.50/case.

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