Final Answer:
The total cost of producing n copies with a res copy machine is given by the formula:C(n) = C(1) + (n-1) * (C(1) + D)
where C(1) is the unit cost of producing one copy, and D is the depreciation cost per copy.
Step-by-step explanation:
To determine the total cost of producing n copies with a res copy machine, we need to consider two factors: the unit cost of producing one copy (C(1)), and the depreciation cost per copy (D). The unit cost is the cost of producing one copy, and the depreciation cost is the cost of using the machine to produce each copy.
The formula for the total cost of producing n copies is:
C(n) = C(1) + (n-1) * (C(1) + D)
This formula can be derived by considering the cost of producing the first copy (C(1)), and then adding the cost of producing each additional copy (n-1) times the depreciation cost per copy (D).
For example, if the unit cost of producing one copy is $10, and the depreciation cost per copy is $2, then the total cost of producing 5 copies would be:
C(5) = $10 + (5-1) * ($10 + $2) = $10 + 4 * ($10 + $2) = $10 + $40 = $50
Therefore, the total cost of producing 5 copies with this res copy machine would be $50.