2. (25 points)

Assume that the total benefit from a continuous decision, involving a control variable Q, is TB(Q) = 25Q - 2.5Q² and the associated total cost is TC(Q) = 3 + 2Q².

With the total benefit and total cost functions (equations) given above:

(a)Estimate the value of net benefits when the control variable Q is 3. Clearly show your steps and calculations.

(b)Estimate the level of control variable Q that maximizes net benefits. Clearly show your steps and calculations.

(c) Provide a mathematical justification that net benefits are maximized at your determined level of the control variable Q in (b) above.