Ho Siong Nam: Tugasan 3

Part1 (a)

Demand of the computer decreases as its selling price increases. In other word, the higher the selling price, the lower the quantity demand.

Part 1 (b)
Profit per unit of computer = s - 50

Total yearly profit,
Y = (s - 50) x d

Y = Total yearly profit
s = Selling Price
d = demand

From the graph in Part 1 (a), we can see that there is a linear relationship the demand and the selling price. Therefore, we can use a straight line equation to represent this relationship.

First of all, let's find the gradient and the y-intercept of the graph

Then let's form the linear equation of the graph

Substitute this into the equation of yearly profit

Y = Yearly profit
s = selling price

Part 1 (c)
Finding the maximum yearly profit

Method 1: By using calculus

Y is maximum (or minimum) when dY/ds = 0

Therefore, yearly profit Y is maximum when the selling price s = 175.

This implies that when the selling price for the computer is RM175 per unit, the company will have the maximum profit potential.

Method 2: Completing the square
We can also find the maximum profit by using the completing the square method.

Maximum profit, Y = RM312,500 when
s-175 = 0
s=175

When the selling price s = RM175, the profit is maximum.

Part 1 (d)
The number of computer,

d = -20s + 6000

For maximum profit, s = RM175

d = -20(175) + 6000
d = 2500 unit.

The number of the computer components to be manufactured by the company in order to gain maximum profit,
d = 2,500 units

Part 2 (a)
Total amount of interest incurred for each choice of repayment period and their corresponding amount of loan is as follow:

Part 2 (b)(maybe this is wrong)
The average interest rate per month is as follow:

Since the interest rate is constant over time, hence the average interest per month remain the same every month. The average interest per month is also directly proportional to the amount of loan.

Correction
A user point out that this question ask for the average interest rate per month but not the average interest per month. If this is the case, then the table should look like below:

Comment: The interest rate is the same for any term of loan and it's affected by the amount of loan. This interest rate (24% per annum) is too high for a normal bank loan

Part 2 (c)
The amount of yearly repayment for each choice of repayment period up to 5 years for loan amounts from RM10 000 to RM100 000 is as follow: This table result also have some wrong
For total annual payment for 12 months, the payment are

12408, 18600, 24804, 31008, 37200, 43404, 49608 .....

T2 - T1 = 18600 - 12400 = 6192
T3 - T2 = 24804 - 18600 = 6204
T4 - T3 = 31008 - 24804 = 6204
T5 - T4 = 37200 - 31008 = 6192
T6 - T5 = 43404 - 37200 = 6204
T7 - T6 = 49608 - 43404 = 6204

Part 2 (d)(i)
The company allocated 20% of the profit made on loan repayment.

From the table above, we find that, if the company allocate RM40,000 for loan repayment, the amount of loan it can take for repayment period, 1, 2, 3, 4, and 5 year are as follow:

Part 2 (e)