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.

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

(b)Determine the level of control variable Q that maximizes total benefit. Clearly show your steps and calculations.

Estimate the total fixed cost and total variable cost when the control variable Q is 3. Clearly show your steps and calculations.