CB2203 Data-Driven Business Modeling Assignment 2
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CB2203 Data-Driven Business Modeling
Assignment 2
Question 1
City Manufacturing has four machines for producing a particular computer chip. The production manager has to decide on the machine(s) to use for producing 1650 units of the chip. Machine 1’s production capacity is between 300 and 1500 units. Machine 2 and/or Machine 3 can be used only if Machine 1’s production is greater than or equal to 1000 units. Machine 4 can be used with no restrictions and can make any number of units.
City Manufacturing has to pay a fixed cost if the machine is in operation. In addition, a variable cost per unit will be incurred.
Machine |
Fixed cost ($) |
Variable cost per unit ($) |
Min. production |
Max. production |
1 |
500 |
2.00 |
300 |
1500 |
2 |
800 |
0.50 |
500 |
1200 |
3 |
200 |
3.00 |
100 |
800 |
4 |
50 |
5.00 |
- |
- |
The objective of City Manufacturing is to minimize the total cost by meeting the production requirements.
(a) Write down the integer linear program to determine the optimal production plan.
[Hint: Use an additional binary variable to indicate when Machines 2 and 3 can be used.] (25 marks)
(b) Develop an Excel spreadsheet model and use Solver to compute the optimal production plan and the minimum total cost. (Request Excel “Keep Solver Solution”, and generate “Answer Report”) (You have to submit the Excel file for grading. Screencap the “Solver Parameter” sub-window whenever appropriate.) (10 marks)
Question 2
The following linear program model is used to optimize the production of four products (X1, X2, X3 and X4), with two different manufacturing processes and two different material requirements.
Max Z = $48X1 + $52X2 + $57X3 + $60X4 (Total profit)
s.t. 4X1 + 2.1X2 + 2.6X3+ 3.9X4 < 500 (Process 1)
3.5X1 + 4.6X2 + 3.5X3+ 1.9X4 < 600 (Process 2)
15X1 + 21X2 + 19X3+ 22X4 < 3500 (Material A)
7.5X1 + 11.5X2 + 9.5X3+ 10.6X4 < 1600 (Material B)
X1, X2, X3, X4 > 0
The linear program model is solved using Excel Solver and sensitivity reports are given as below:
Adjustable Cells
Cell |
Name |
Final Value |
Reduced Cost |
Objective Coefficient |
Allowable Increase |
Allowable Decrease |
$B$15 |
Product 1 |
29.10 |
0 |
48 |
25.35 |
1.68 |
$C$15 |
Product 2 |
0 |
-17.02 |
52 |
17.02 |
1E+30 |
$D$15 |
Product 3 |
139.37 |
0 |
57 |
1.40 |
7.23 |
$E$15 |
Product 4 |
5.44 |
0 |
60 |
5.14 |
4.56 |
Constraints |
||||||
|
|
Final |
Shadow |
Constraint |
Allowable |
Allowable |
Cell |
Name |
Value |
Price |
R.H. Side |
Increase |
Decrease |
$F$18 |
Process 1 |
500 |
0.72 |
500 |
268.93 |
34.29 |
$F$19 |
Process 2 |
600 |
2.16 |
600 |
12.97 |
135.19 |
$F$20 |
Material A |
3204.35 |
0 |
3500 |
1E+30 |
295.65 |
$F$21 |
Material B |
1600 |
5.01 |
1600 |
141.53 |
48.98 |
Based on the sensitivity reports, answer the following questions:
(a) What is the optimal production mix and total profit? (5 marks)
(b) Holding all other factors remain unchanged, what is the profit contribution of Product 1 so that the optimal production mix remains the same. (2 marks)
(c) Which is the most valuable resource to the firm? Why? (2 marks)
(d) One of the four products is not produced in the optimal mix. What would the profit become if one unit of such a product was produced while other conditions remain the same? (2 marks)
(e) If the manufacturer can obtain an extra amount of 100 units of Material B at the price of $4.0 each, should he do so or not? Explain. What is the new total profit? (4 marks)
2023-11-28