AMA 502 Assignment 2 Semester 1, 2020–2021
Due date for submission: December 4, 2020, 2:00 pm. Late assignment will lose credits.
1. (10 points) Solve the following linear programming problem using simplex method.
Maximize x1 + 4x2 + 5x3
Subject to 3x1 − 5x2 + x3 ≥ 30,
x1 + 2x3 ≤ 20,
2x1 + 4x2 + 6x3 ≤ 50,
x1, x2, x3 ≥ 0.
2. (10 points) Suppose that a firm can produce a specialty product in either of its two plants:
Plant Production capacity (in packages) Production cost per package
A 1800 25
B 1700 24
Four chain stores would like to purchase the products. Their demands and the prices they offer are:
Store Max demand (in packages) Offered price per package
1 900 52
2 800 54
3 950 50
4 1050 53
Moreover, the shipping cost per package from a plant to a store is:
Plant A Plant B
Store 1 7 10
Store 2 6 8
Store 3 9 8
Store 4 6 9
Determine a delivery schedule that will maximize the total profit for the firm. [Hint: You may want to
formulate this as a transportation problem.]
3. (15 points) The following table shows the activities of a certain project, together with their normal
duration, crash times and crash costs.
Activity Immediate Predecessors Normal Time Normal Cost Crash Time Crash Cost
A none 3 110 2 160
B none 4 110 3 140
C A 5 160 2 280
D A,B 7 300 5 380
E C 4 700 3 720
F D,E 9 600 6 900
The terminating activity is F .
(i) Draw the network diagram representation of the project.
(ii) Find the critical path, the project completion time and the corresponding cost under normal costs.
(iii) Suppose that the project is required to be completed in 18 days. In order to yield the minimum
project cost, which activity should be crashed and by how much? What is the final cost?
AMA 502 Assignment 2
4. (15 points) A certain product is used up at an average rate of 300 units per day. The holding cost per
unit inventory per day is $1, and the shortage cost per unit inventory is $5. The cost for placing an
order is $60. Moreover, from historical record, the demand during lead time is uniform over the range
(0, 80) units.
• Show that the optimal quantity to order, y∗, exists and is unique;
• write down the equations that the optimal (y∗, R∗) has to satisfy;
• write down the algorithm initialization and the formulae for the iterates;
• compute the optimal (y∗, R∗) to 2 decimal places.
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