Question

A cheese producer sells a cheddar into two segments. The linear price-demand function for each segment is defined by A1= 1,057, B1= 12 and A2= 773, B2= 7. From a production quantity of 750 Kg the manufacturer decides to allocate 550 to segment 1 and 200 to segment 2. Determine the market price for each segment. Then, what is the total revenue (both segments)?

Answer 1

Solution :

Given That :

As,we know the linear Demand curve formula is

Q = A-BP

Here

Q Quantity

A All factors affecting the price other than price

B slope of the demand curve

P Price of the goods

Here in Segement 1   

Q1 = 550

A1 = 1057

B1 = 12

Hence

Q1 = A1- B1P1

550 = 1057 - 12P1

P1 = (1057-550)/12

P1 = 42.25

Similarly in Segement 2

Q2 = 200

A2 = 773

B2 = 7

Hence

Q2 = A2 - B2P2

200 = 773 - 7P2

P2 = (773 - 200)/6

P2 = 95.5

Hence market price in segement 1 is 42.25 and in Segment 2 it is 95.5

Toal Revenue = Q1XP1+Q2XP2  

550X42.25 + 200X95.5   

Total Revenue = 42337.5