Question

a. The price, p (in rands) and the quantity sold of Scientific calculators obey the demand equation, x = -40p + 700 where 0 <p s 30 Express the revenue R as a function of x. (3 Marks) b. What is the revenue if 50 lab coats are sold? (2 Marks) What quantity x maximises revenue? What is the maximum price? (4 Marks) d. What price should the company charge to maximise revenue? (2 Marks) e. What price should the company charge to earn at least R4000 in revenue? (7 Marks) [Sub Total 18 Marks] C.

Answer 1

Demand function x= -40þ+ 700 plice Þ= 700-X 40 @ Revenue R(x) = quantity & price xp R(x) = x x(100-*) 700x-x? 40 2 Revenue RE 700X-X 40 lands 6 quantity sold Revenue x=50 lab Coate 700 (50)- 50% 812.5 lande 40 dR dR dx 20 and © When revenue attains maximum, dacato dr dx 700 - 2X=0 x= 350 -2 40 <o dan dx² Therefole helenue attaing maximum when 1x=350 lab Coats Maximum Revenue = 700 (350) -350 = 3062.5 clands 40 We have p= 700-2 Price is maximum luhen x=0, therefore maximum plie = 20 = 17.5 30 hands

a when revenue is maximized, X = 350 Therefole price += 700-350 8.75 lands 40 @ we want to find plice plice p such that the revenue Rz4000 But from part @ we found that maximum revenue that Can be attained is 3062.5 lands. Hence we conclude that there is no plice which earns the revenue of atleast R4000.