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Decision Support Systems and Data Mining
1. Consider the following simple present value model:
Present value is a financial model which helps to calculated the time value of money based on the payment amount in the future subject to a particular interest rate and duration of the time. Following is the simple present value model, which calculates P, present value, as the rate of F, the future value (payment amount), over (i+1), interest rate plus one powered by n, the duration of the time.
P = F/(1 + i) n
Suppose F = £10000, i = 8% and n = 10 years, then determine the present value P using Excel, to solve the problem as described below:
1. a. without using any of the built-in financial functions
1. b. with using Excels built-in financial functions
You should produce the formulas in the same worksheet; entitle it Q1.
[10 MARKS IN TOTAL, 5 Marks for each part]
2. Using the Formula produced in 1 (use cell referencing to produce these):
2. a. Construct a table of values for P, on a new worksheet with F varying in steps of £300 from £0 to £15000 and i varying in unit steps from 3% to 15%. (n fixed here at 10 years); entitle the worksheet Q2a.
2. b. Copy the worksheet to 9 other worksheets and hence create a workbook of present values with F varying in steps of £300 from £0 to £15000, i varying in unit steps from 3% to 15% and n varying in yearly steps from 1 to 10 years.
You should now have a workbook consisting of 10 sheets; entitle them Q2b1, Q2b2, Q2b3, … Q2b9.
[20 MARKS IN TOTAL, 2 Marks for each correct worksheet]
3. Consider the following problem introduced:
A factory makes 3 components, A, B and C using the same production process for each. A unit of A take 1 hr, a unit of B takes 0.75 hrs and a unit of C takes 0.5 hrs. In addition, C has to be hand finished, an activity taking 0.25 hrs per unit. Each week total production time (excluding hand finishing) must not exceed 300 hrs and hand finishing must not exceed 45 hrs.
The components are finally assembled to make two finished products. One product consists of 1 unit of A and 1 unit of C selling for 30 pounds whilst the other consists of 2 units of B and 1 unit of C and sells for 45 pounds. At most 130 of the first product and 100 of the second product can be sold each week.
3. a. Formulate the problem of planning weekly production to maximise total proceeds as a linear programming problem in 2 variables and obtain the solution graphically.
3. b. Revise the price for the first product from £30 to £35 and resolve the problem graphically to find out and show the new optimum solution. Compare the old and new solutions with respect to the impact of the price.
3. c. Revise the limit for the number of the second product from 100 to 120 and resolve it graphically to find out and show the new optimum solution. Compare the old and new solutions with respect to the impact of the capacity limit.
3. d. Solve the problem with MS Excel Solver in-built functionality for all three cases to verify your solutions found graphically.