A Leading mobile phone manufacturer is about to introduce a new series, initially, they are launc...

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.

Table 1

1. Develop a joint total revenue function for sales of the four different models.
2. Develop an annual total cost function for manufacturing the four models.
3. Develop the profit function for sales of the four models.
4. Calculate the annual profit if the firm sells 9000, 12000, 45000 and 22000 units, respectively, of the four models?

Part – B:

In manufacturing 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;

1. Develop the function C = f(x) which expresses annual cost.
2. Calculate f(280,000)? What does f(280,000) represent?
3. State the restricted domain and restricted range of the function if maximum production capacity is 850,000 units per year

   Question No. 5:

   Part – A:   

   A corporate agricultural organization has three separate farms which are to be used during the coming year. Each farm has unique characteristics which make it most suitable for raising one crop only. Table below indicates the crop selected for each farm, the annual cost of planting 1 acre of the crop, the expected revenue to be derived from each acre, and the fixed costs associated with operating each farm. In addition to the fixed costs associated with operating each farm, there are annual fixed costs of $75,000 for the corporation as a whole.

   Farm	Crop	Cost/Acre (cj)	Revenue/Acre (rj)	Fixed Cost (Fj)
   1	Soya beans	$900	$1,300	$150,000
   2	Corn	$1,100	$1,650	$175,000
   3	Potatoes	$750	$1,200	$125,000

   Table 2

4. Determine the profit function for the three-farm operation.
6. What are the expected profits for the program if the board of directors has voted on the following planting program for the coming year; 1,000 acres will be planted at farm 1, 1,600 at farm 2 and 1,550 at farm 3?
8. A Summer drought has resulted in the revenue yields per acre being reduced by 20, 30 and 10 percent, respectively, at the three farms. What is the profit expected from the mentioned planting program?

   Part – B:   

   Given,fa,b,c,d=3a2b+bc-2ad2, Evaluate f-2,2,-4,-3 and f2,3,4,5

   Part – C:

   The function q = 230,000 -28p is a demand function which expresses the quantity demanded of a product q as a function of the price charged for the product p, stated in dollars. Determine the restricted Domain and Range of the function.