Final answer:
The original profit before a 10% decrease that results in a net profit of $400 is approximately $444.44 per unit. Theoretically, future profit could continue to accumulate indefinitely, so there is no precise calculation for a finite total possible future profit from this tool. None of the provided answer choices offer a correct total future profit as they all represent finite values.
Step-by-step explanation:
If a hire tools firm's net profit decreases by 10% per unit gain on a certain tool and the net gain on this tool for the year is $400, we need to calculate the original profit before the 10% decrease to determine the possible total of all future profit from this tool.
Let x represent the original net gain before the 10% decrease. The 10% decrease can be represented as 0.10x. The net gain after the decrease is therefore x - 0.10x = 0.90x, and we know this equals $400. To find the original gain x, set up the equation:
0.90x = $400
Solving for x yields x = $400 / 0.90 = $444.44 approximately.
According to the question, this is the net gain per unit, and we want to know the total future profit if the profit per unit moves in increments of this original gain. We calculate the future profit by multiplying this per unit gain by a large enough number so that the profit no longer grows. Assuming the firm experiences this net gain on each subsequent sale and the market does not change drastically, theoretically, the profit could continue to accumulate indefinitely. However, business conditions change, and this model does not take into account market saturation, increased competition, or changes in demand.
Hence, there is no finite 'possible total of all future profit' that can be precisely calculated, and none of the answer choices (a) $4,000 (b) $4,400 (c) $4,800 (d) $5,200 provided indicate a projected total future profit, as they all represent finite values.