At a production level of 1400 items, the total cost is $7250 and the marginal cost is $25. Use this information to estimate the costs of producing the following number of items. Your answers should be whole numbers.
a) 1401 items .
b) 1399 items .
c) 1450 items .
I assume the "total cost" is "total fixed cost" since the marginal cost is higher than the "total cost" divided by the number of items.
So at the production level of 1400 items, total cost = total fixed cost + n*marginal cost
where n=number of items to be produced,
marginal cost = $25, and
total fixed cost = $7250
To estimate the costs of producing different numbers of items, we can use the concept of marginal cost. Marginal cost refers to the cost of producing an additional unit of a product. In this case, we know that the marginal cost is $25.
Given that the total cost at a production level of 1400 items is $7250, we can calculate the average cost per item by dividing the total cost by the number of items produced.
Average cost per item = Total cost / Number of items
So, the average cost per item is $7250 / 1400 ≈ $5.18 (rounded to two decimal places).
To estimate the costs of producing different numbers of items using the marginal cost, we can follow these steps:
a) 1401 items:
To estimate the cost of producing 1401 items, we add the marginal cost ($25) to the total cost of producing 1400 items.
Cost = Total cost + Marginal cost = $7250 + $25 = $7275
Therefore, the estimated cost of producing 1401 items would be $7275.
b) 1399 items:
To estimate the cost of producing 1399 items, we subtract the marginal cost ($25) from the total cost of producing 1400 items.
Cost = Total cost - Marginal cost = $7250 - $25 = $7225
Therefore, the estimated cost of producing 1399 items would be $7225.
c) 1450 items:
To estimate the cost of producing 1450 items, we first calculate the additional number of items beyond 1400 (50 items in this case). Then, we multiply the marginal cost ($25) by the additional number of items and add it to the total cost of producing 1400 items.
Additional items = 1450 - 1400 = 50
Cost = Total cost + (Marginal cost * Additional items) = $7250 + ($25 * 50) = $7250 + $1250 = $8500
Therefore, the estimated cost of producing 1450 items would be $8500.