2. (25 points) Assume that total benefit from a continuous decision, involving a control variable Q, is TB(Q) = 24Q - 3.25Q2 and the associated total cost is TC(Q) = 4.50 + 3.50Q2. With the total benefit and total cost functions (equations) given above: (a) Determine the level of control variable Q that maximizes total benefit. Clearly show your steps and calculations in 2 decimal points. (b) Provide a mathematical justification (or sufficient condition) that total benefits are maximized at your determined level of the control variable Q above. Clearly show your steps and calculations. (c) Estimate the level of control variable Q that maximizes net benefits. Clearly show your steps and calculations in 2 decimal points. (d) Estimate the total fixed cost and total variable cost when the control variable Q is 3. Clearly show your steps and calculations in 2 decimal points