a) The demand function of a commodity is described by the experimental function

P=10.5e^-0.1Q

Where Q is the quantity demanded and TR = total revenue.

Determine

(i) The quantity for which the total revenue is maximized

(ii) The maximum revenue

(Hint: revenue is maximized when dTR =0

dQ

b) In making a certain item, a business has discovered that the demand function for the item is represented by

p=50

x

The cost function of producing x items is given by C=0.x+500

(i) Find the price per unit that yields a maximum profit ()

(ii) Find the output level that maximizes profit

(iii) Find the maximum profit ()

(iv) Show that the second-order condition has been fulfilled