FINANCIAL MATHEMATICS

Financial Mathematics



Financial Mathematics and Business Statistics

Question 1

Scenario

Crisis Continues

Slow Recovery

Medium Recovery

Fast Recovery

Probability

20%

15%

50%

15%

Demand

40,000

65,000

105,000

250,000

Total Cost

58000

94250

152250

362500

The company should consider the medium recovery demand level, which has 50 % probability for the next year. The company should order the stock at 105000 demand level because the chances are higher than other demand levels. The pessimistic approach can bring negative consequences such as if the company order the stock at low level and but the economy recovers quickly, then there will be difficulty in buying again the stocks. Either there will be shortage or the prices will increase when the sudden demand will increase. Similarly, optimistic approach will bring hard time to company. If the company buys large number of stock, but the economy does not recover, the stock will become expense for the company and it will be difficult to sell products without much demand from the public. Therefore the company should focus the middle level of demand in order to operate efficiently.

The company has negotiated their main supply to decrease the cost of stocks from $280 to $190. The company can save good amount of money by taking advantage of this negotiate and order the stocks.

Question 2

In this question we will be answering how the furniture manufacturer can maximize its profits and which products he should focus more in order to reach its higher profit point. For this task we have used excel solver (Linear Programming technique). Following are the constraints that will be used in order to determine the order quantity resource placement to achieve high profit.

Max: 3500Square + 3000Round + 1500Rectangular + 2000Elliptic

11 Round + 12Elliptic <= 52000

7 Square + 8 Rectangular <= 36000

6 Square + 4 Round + 9 Rectangular + 8 Elliptic <= 48500

1.5 Square + 2.75 Round + 2 Rectangular + 3.5 Elliptic <= 20000

Following are the results that were achieved when we implemented these constraints:

Square

Round

Rectangular

Elliptic



RHS

Dual

Maximize

3500

3000

1500

2000

Wood

0

11

0

12

<=

52000

0

Metal

7

0

8

0

<=

36000

0

Other Materials

6

4

9

8

<=

48500

488.0952

Labor

1.5

2.75

2

3.5

<=

20000

380.9524

Solution->

5083.333

4500

0

0

31291670

The above table states that the company should focus on the square and round tables as there is more demand for this product. Also these tables are providing more profit to the company. If they will make 5083.333 round table and 4500 of round tables they will earn a profit of $ 31,291,670. They should focus on these products and use their resources for the production of these products. All the formulations of the strategy is present in Appendix A.

Question 3

Total exposure on Alan's Salary= £52,000*2.5= £130,000

Total exposure on Karen's Salary= £38,500*2.5= £96250

The total exposure on individual basis is calculated to be= £130,000+£96,250= £226,250

If both of these individuals open up a bank account and jointly deposit their salary into one account then their exposure can be increased as illustrated below:

(£52,000+£38,500)*3.25= £294,125

Thus the maximum exposure (borrowing) is calculated to be £ 294,125

Keeping in mind their financial position, I would recommend them to borrow the minimum amount of exposure that is applicable on their individual salary. This is because, looking at their financial positions, the per month salary of Alan 4334 and Karen is 3208 which is comparatively low to have a stable ...