BUSINESS MATHEMATICS

CA 1- Individual Assignment

Students name: ZHOU JUNHAO

FIN Number: G0877383T

Part 1 question 1
A.[pic]
⇒ X=4

B.[pic] ⇒ [pic] ⇒ [pic]

C. [pic] ⇒ [pic]
D.[pic]
⇒ [pic]
⇒ 2x=[pic]
⇒ X=5000

E. O[pic]

⇒ [pic]
Let [pic] than [pic]
⇒[pic] ⇒[pic]
⇒ [pic]
⇒ K=[pic]
When t=12, we have [pic]≈874

Part 2 question 2
A.[pic]
Domain[pic] Range[pic]

B. Monthly Function is [pic]×4 Annual Function is [pic]×48
C. let cost function be [pic] [pic] Domain[pic] Range[pic]

D. Let profit function be [pic] [pic]=[pic] [pic]=[pic] Domain[pic] Range[pic]
Part 2 question 3
[pic]
[pic]
⇒ [pic]
⇒ 0=3[pic]0
⇒ X=[pic] or X=10
[pic] So X=10
When X=10
P=[pic]
P=60

[pic] P=100=[pic]
⇒[pic]
⇒X=20 or-30
[pic]So X=20

Part 3 question 4
A.
Based on the question 2 equation, we came to the conclusion, by analyze the equation. TriOptics should expand advertising. As we know the Management has decided run a maximum of 10 hours of adverting per week which is now is 60 hours per week. According to the [pic] run more adverting Function[pic]will increase but Function [pic] also increase .then we using [pic] it give us the conclusion the weekly profit is gets higher than before[pic]. So in this situation there is profit by expand advertising. Therefore, those equation can let us know if TriOptics expand advertising than the profit is increase.[106 words]
B. Based on the question 3 equation, we can give a recommendation by analyze the situation which is when the price increase to 100, the demand X is still remain the same in first equation[pic]. So if The COE of TriOptics wants to output levels for the new market, the supply will increase but the demand X is still remain the same in this new market. Therefore,