MGM3164 – QUANTITATIVE METHODS FOR BUSINESS
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MGM3164 – QUANTITATIVE METHODS FOR BUSINESS
Test – 2 (28 December 2019)
1) Mohd Danial Zulfaris, a student from UPM, starts a bags manufacturing shop. He decides to start manufacturing deluxe and standard bags. The manufacturing operation consists of three stages: cutting, assembly, and painting. The production hours for table and chair are as follows:
|
Cutting (time in hours per unit) |
Sewing (time in hours per unit) |
Finishing (time in hours per unit) |
Standard bag |
5 |
8 |
2 |
Deluxe bag |
6 |
7.5 |
3 |
The production man-hours available each week in cutting is 240 hours, in sewing is 320 hours, and 300 hours in finsihing. For each deluxe bag that is produced four standard bags must be produced. The profit margin for each deluxe bag is RM 200 and for each standard bag is RM100. Find the number of deluxe and standard bags to be produced to maximize the profit (via a graph).
2) Suniljeet Singh Restaurant has full-time and part-time employees to run the business. There are four full-time employees. The remaining are part-time employees. The four full- time employees work for 8 hours per day and part-time employees work for 4 hours per day. The restaurant starts at 8 am and closes at 10 pm. Two full–time employees come at 8 am and the remaining two come at 12 noon. The full-time employees work for 4 hours, take a 2- hour break and continue for another 4 hours. For example, the full-time employees who come at 8 am, work until 12 noon, take a 2-hour break and work from 2 pm to 6 pm. The part-time employees do not have any break. The part-time employees can come during any time slot, i.e., at 8 am, 10 am, 12 noon, 2 pm, 4 pm, or 6 pm. The full-time employees are paid RM 160 for 8 hours and part-time employees are paid RM 80 for 4 hours. The minimum number of employees required in a day is as follows:
Time slot |
Minimum number of employees |
8am – 10am |
11 |
10 am – 12 noon |
8 |
12 noon – 2 pm |
6 |
2 pm – 4 pm |
9 |
4 pm – 6 pm |
10 |
6 pm – 8 pm |
8 |
8 pm – 10 pm |
6 |
Formulate a LP model to minimize the wages (salaries paid to the employees).
Q 3) The following linear programming problem has been solved by The Management Scientist. Use the output to answer the questions.
LINEAR PROGRAMMING PROBLEM
MAX 25X1+30X2+15X3
S.T. 1) 4X1+5X2+8X3<1200
2) 9X1+15X2+3X3<1500
OPTIMAL SOLUTION
Objective Function Value = 4700.000
Variable |
Value |
Reduced Costs |
---------- |
-------- |
------------------ |
X1 |
140.000 |
0.000 |
X2 |
0.000 |
10.000 |
X3 |
80.000 |
0.000 |
Constraint ------------- 1 2 |
Slack/Surplus ---------------- 0.000 0.000 |
Dual Prices -------------- 1.000 2.333 |
OBJECTIVE COEFFICIENT RANGES
Variable |
Lower Limit |
Current Value |
Upper Limit |
---------- |
--------------- |
---------------- |
--------------- |
X1 |
19.286 |
25.000 |
45.000 |
X2 |
No Lower Limit |
30.000 |
40.000 |
X3 |
8.333 |
15.000 |
50.000 |
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
------------ --------------- ----------------- ---------------
1 |
666.667 |
1200.000 |
4000.000 |
2 |
450.000 |
1500.000 |
2700.000 |
a. Give the complete optimal solution.
b. Which constraints are binding?
c. What is the dual price for the second constraint? What interpretation does this have?
d. Over what range can the objective function coefficient of x2 vary before a new solution point becomes optimal?
e. By how much can the amount of resource 2 decrease before the dual price will change?
f. What would happen if the first constraint's right-hand side increased by 700 and the second's decreased by 350?
2022-09-16