Suppose that the total cost to produce 200 units of a consumer item is C(200) = $3,789 and that the marginal cost at this production level is C'(200) = 16 dollars per unit made. Use this information to estimate the total cost C(205).
d C/ du = 16 $/unit
d C = 16 du = 16 (205- 200) = 80
C(205) = C(200) + 80 = 3789 + 80
To estimate the total cost C(205), we can use the marginal cost at production level 200 and apply it to the additional 5 units produced.
The marginal cost represents the additional cost to produce one more unit. In this case, we are given that the marginal cost is $16 per unit.
From this information, we can estimate the additional cost to produce 5 more units by multiplying the marginal cost by the number of additional units (5):
Additional Cost = Marginal Cost * Additional Units
= $16 * 5
= $80
Now, to estimate the total cost C(205), we need to add the additional cost to the total cost at production level 200:
Total Cost C(205) = Total Cost C(200) + Additional Cost
= $3,789 + $80
= $3,869
Therefore, the estimated total cost C(205) is $3,869.
To estimate the total cost C(205), we can use the concept of marginal cost. Marginal cost represents the additional cost incurred when producing one additional unit of a product.
Given that the marginal cost at the production level of 200 units is C'(200) = 16 dollars per unit, we can assume that the additional cost per unit remains constant for a small increase of 5 units. Therefore, we can estimate that the total cost to produce the 205 units will increase by 5 times the marginal cost per unit.
Mathematically, we can calculate it as:
Additional cost = Marginal cost per unit * Additional units
Additional cost = 16 dollars per unit * 5 additional units = 80 dollars
Now, to estimate the total cost C(205), we need to add this additional cost to the total cost of producing 200 units (C(200) = $3,789).
Total cost C(205) โ C(200) + Additional cost
Total cost C(205) โ $3,789 + $80
Total cost C(205) โ $3,869
Therefore, the estimate for the total cost C(205) is approximately $3,869.