Answer to Question #146941 in Linear Algebra for saba

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.

Models

Infinity A Pro Max
Infinity A Pro
Infinity A
Infinity A Lite
Selling Price (in dollars)
500
400
340
220
Material Cost /unit (in dollars)
220
190
150
90
Labor Cost/unit (in dollars)
90
65
65
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

The data of variable costs and selling price is provided only for a single model let it be the same for all the models with variation +100 each (assumed).

So

Infinity A Pro B Pro C Pro D Pro 

selling price 500 600 700 800

material cost 220 320 420 520

labor cost 90 190 290 390

a) revenue

Let sales of models A, B, C, D be a, b, c, d units respectively.

Revenue = $(500a + 600b + 700c + 800d)

b) annual cost = fixed cost + variable cost

= 540000 + ((220 + 90)a + (320 + 190)b + (420 + 290)c + (520 + 390)d) =

= 540000 + 310a + 510b + 710c + 910d

c) profit = revenue – cost

= (500 – 310)a + (600 – 510)b + (700 – 710)c + (800 – 910)d – 540000 =

= 190a + 90b – 10c –110d – 540000

d) the firm sells 9000 units of a, 12000 units of b, 45000 units of c and 22000 units of d

profit = 190*9000 + 90*12000 – 10*45000 – 110*22000 –540000 = –620000