代写Quantitative Methods

Quantitative Methods

Question 1    (10 points)

Using the “supermarket data” in the course, assuming that the transaction amount in the sample data has passed the validity test, the “amount” is considered to be Normal Distribution, and the sample data can directly and fully describe the population parameters. Please calculate:

(1) The probability that the customer will buy between $40 and $60.

(2) The supermarket is planning to reward customers with a large amount of single transaction. If supermarket wants to reward no more than 5% of customers, how should they set the reward criteria for the purchase amount.

Question 2   (15 points)

A family has a 30-year $880,000 mortgage at 8% compounded monthly.

(1) Find the monthly payment and the total interest paid

(2) After 10 years, suppose the family decides to add an extra $150 to its mortgage payment each month. How long will it take the family to pay off the remain mortgage?

(3) How much interest will the family save?

Question 3   (15 points)

The Pacific Paper Company produces paper rolls with a standard width of 20 feet each. Special customer orders with different widths are produced by slitting the standard rolls. Typical orders (which may vary from day to day) are summarized in the following table:

Order	Desired Width (ft)	Desired Number of Rolls
1	3	180
2	5	200
3	7	300
4	10	160

The objective is to satisfy the above orders with the minimum possible wastage.

Formulate the solution and constrains by using linear programming technique.

Question 4   (20 points)

A Company produces five products using two machines, two raw materials and labour. The profit per unit for each product, availability of each resource and the requirement of each resource for each product are as below Excel sheet. In addition, each product has a maximum market demand. The company does not wish to exceed this for any product. The objective is to maximise profit subject to availability of resources and market demands.

 

(1) Reformulate the problem in Excel Solver. Present your solver screen.  

(2) Generate and present your Sensitivity report.

(3) As a factory manager, generate a report focus on resource usage and availability.

(4) Consider the market demand and pricing, generate a report of profitability.

Question 5   (15 points)

There is a material, which demand is：5000 unit/year. We have Reorder Cost: $10，Holding Cost：$4/unit per year. The supplier offers variable Unit Cost as below：

Q<1000, UC=$6.8; 999<Q<2000，UC=$6.5; 1999<Q<3000，UC=$6; Q>2999单位, UC=$5.8

Please help to determine the optimal order quantity

Question 6   (10 points)

 A company sales product A to its customer. The company forecasts the monthly demand of  product A d=11107 units, s_d=3099 units. The cost of A is UC=0.11 $/unit, the reorder cost RC = 10 $/order, the holding cost of product A is 20% yearly of its value. The leading time of ordering is constant, LT=1.5 month. The company wants the service level to achieve 75%. Please give the optimal inventory policy for the company. (The reorder quantity and ROL, we have Z=0.67 for SL>=75%)

Question 7   (15 points)

Based on the learning of this course, please give some of your opinion on the following topics:

(1) what is your understanding of quantitative methodology.

(2) what is the difference between mathematics programming and computer simulation.