Control Variable Q= Total Benefits TB(Q)= Total Cost TC(Q)= Net Benefits NB(Q)= Marginal Benefits MB(Q)= Marginal Cost MC(Q) =Marginal Net

100 1200 900 - 257.5 70 -

104 2110 - - - 90 -

108 2900 - - - 110 -

112 3570 - - - 130 -

114 3875 - - - 140 -

115 4020 - - - 145 -

116 4157.5 - - - 150 -

120 4587.5 - - - 170 -

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