We consider the cost function C(q) and the revenue function R(q) for a manufacturer, where q is the number of units of a certain item. Both C(q) and R(q) are in dollars.

(a) The demand/supply equilibrium is at q = 42. The manufacturer is currently producing 41 items, with C'(41) = 21 and R'(41) = 19. Should he meet the market expectations of producing 42 items? You must explain your reasoning.

(b) Given that C(37) = 3700, C'(37) = 17, and C" < 0. Which of the following are possible values for C(40) and which are impossible? You must carefully justify your finding.  

i) 3739 

ii)3751 

iii)3765