A Leading mobile phone manufacturer is about to introduce a new series...
Part â€“ A:Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Marks [3]
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.
Â 
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
 Develop a joint total revenue function for sales of the four different models.
 Develop an annual total cost function for manufacturing the four models.
 Develop the profit function for sales of the four models.
 Calculate the annual profit if the firm sells 9000, 12000, 45000 and 22000 units, respectively, of the four models?
Part â€“ B:Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Marks [2]
In manufacturing a medical equipment, a firm incurs costs of two types. Fixed annual costs of $ 155,000 are incurred regardless of the number of units produced. In addition, each unit produced costs the firm $5. If C equals total annual cost in dollars and x equals the number of units produced during a year;
Â
 Develop the function C = f(x) which expresses annual cost.
 Calculate f(280,000)? What does f(280,000) represent?
 State the restricted domain and restricted range of the function if maximum production capacity is 850,000 units per year