3 A large company in the communication and publishing indust

3. A large company in the communication and publishing industry has quantified the relationship betweent 0.01xDemand for an annual printing of this particular product. The fixed costs per year (i.e, per printing) S50,000 and the variable cost per unit-S40. Q1: Determine the optimal demand? 02: What is the maximum profit that can be achieved? rice-150

Solution

1) P = 150 - 0.01 D where D = demand for an annual printing of this particular product.

Fixed cost (TFC)= $ 50,000

Average varibale cost = $40

Total variable cost (TVC) = (40)(D) = 40 D

So, the total revenue (TR) = P (D)

= 150 - 0.01 D (D)

= 150D - 0.01 D²

Total cost (TC) = TFC + TVC

= $ 50,000 + 40 D

Profit = TR -TC

= (150 D - 0.01 D²) - (50000 + 40 D)

Now, do the first derivative of total profit and equate it with zero.

= 150 - 0.01(2) D - 40

= 110 - 0.02 D = 0

D = 110/0.02

D = 5500 [ Optimal demand]

2.) Maximum profit that can be achieved ,is by putting D =5500 in total profit function:

Total profit = [150 (5500) - 0.01(5500)² ] - [50,000 + 40 (5500) ]

= [825000 - 0.01(30250000)] - [ 50,000 + 220000]

= [825000 - 302500] - [270000]

= 522500 - 270000

= $ 252500 [ Maximum profit that can be achieved]