Final answer:
To determine the production level for maximum profit, calculate the profit function by subtracting total cost from total revenue, find its derivative, and determine the production level that yields the highest profit value among the given options.
Step-by-step explanation:
To find the production level for the maximum profit given the revenue and cost functions R(x) = 2x and C(x) = 0.01x² + 0.5x + 10, we need to calculate the profit function P(x) which is defined as P(x) = R(x) - C(x).
We then find the derivative of the profit function, P'(x), to determine the critical points. Setting P'(x) to zero and solving for x will give us the level(s) of output at which profit is maximized. Examining the given options, we would substitute the values of x into the profit function P(x) to find out which one yields the highest profit. The correct option will have the highest P(x) value when compared to the other choices provided.
Note: As the actual calculations and specific data for each production level were not directly provided, the above-mentioned method outlines the general approach to solving such problems. The specific answer depends on the result of the calculations.