Question

A manufacturer of an external hard disc provided the information that when the price per external hard disk is RM89, then 1 million hard disc will sell. When the price of each hard disc is RM79, then 3 million hard disc will sell. The cost of producing and selling million hard disc is () = 19 + 156.25. a) Find a linear demand function where is the number of millions of hard discs sold and is the price of each hard disc in RM. (3 marks) b) What is the company’s revenue function for this hard disc? (2 marks) c) What is the company’s profit function? (2 marks) d) How many hard discs must be produced and sold so that the company will have a maximum profit? (2 marks) e) What is the price of hard disc when the company is maximizing their profit? (1 mark)

Answer 1

Answer:

a) A linear demand function can be calculated be getting the equation of this line (demand function) using the two point slope formula.

(x0, x1) = (1,3)

(P0, P1) = (89,79)

Linear demand function is given by

p - p0 = p1 - p0/x1 - x0 (x - x0)

p - 89 = 79 - 89/3 - 1 (x - 1)

p - 89 = -5 (x - 1)

=>p - 89 = -5x + 5

p + 5x = 94

p = 94 - 5x (linear demand)

b) REVENUE   Function = Total revenue (tr)

TR = p.x

     ( 94 - 5x ) x = 94 x - 5x2  

c) Profit function = total revenue - total cost

   pie = (94x - 5x2 - (19x + 15625)

= -5x^2 + 75x - 15625

d) we have to find the optimal number of hard discs (x*) at which profit (pie) is getting maximized i.e.

Profit (pie) gets maximum at the point where