Question

A Leading mobile phone manufacturer is about to introduce a new series, initially they are launching 4 models of the same series. The accompanying table summarizes price and variable costs data, combined fixed costs equal $540,000.
Selling Price (in dollars) Material Cost /unit (in dollars) Labor Cost/unit (in dollars)
Infinity A Pro Max 500 220
90
Models Infinity A Pro
400 190 65
Infinity A
340 150 65
Infinity A Lite 220
90
50
Table 1
a) Develop a joint total revenue function for sales of the four different models.
b) Develop an annual total cost function for manufacturing the four models.
c) Develop the profit function for sales of the four models.
d) Calculate the annual profit if the firm sells 9000, 12000, 45000 and 22000 units, respectively,
of the four models?

Answer 1

Given : A Leading mobile phone manufacturer is about to introduce a new series, initially they are  launching 4 models of the same series

To Find :a) Develop a joint total revenue function for sales of the four different models.

b) Develop an annual total cost function for manufacturing the four models.

c) Develop the profit function for sales of the four models.

d) Calculate the annual profit if the firm sells 9000, 12000, 45000 and 22000 units, respectively, of four models?

Solution:

                 

unit sold         A                         B                        C                    D              

Model    Infinity A  Pro   Max Infinity A Pro    Infinity A     Infinity A  Lite

SP             500                        400                     340            220

MC            220                         190                     150             90

LC              90                           65                       65              50

joint total  Revenue function = 500A + 400B  + 340C  + 220D

annual total cost function for manufacturing the four models.

Infinity A  Pro = (220 + 90)A = 310A  

Max Infinity A Pro = (190 + 65)B = 255B

Infinity A =  (150 + 65)C  = 215C

Infinity A  Lite  = (90 + 50)D = 140D

profit function for sales of the four models.

Infinity A  Pro =  500A - 310A = 190A

Max Infinity A Pro =400B - 255B  = 145B

Infinity A = 340C  - 215C = 125C

Infinity A  Lite  =  220D - 140D = 80D

annual profit if the firm sells 9000, 12000, 45000 and 22000 units, respectively, of four models?

Infinity A  Pro =  190*9000 =   1710000

Max Infinity A Pro =  145*12000 = 1740000

Infinity A =125*45000  = 5625000

Infinity A  Lite  =   80*22000 = 1760000

Total Profit =  1710000 + 1740000 + 5625000 + 1760000

= 10835000

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