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CMGT_575_ Final_Exam
Directions: Each submission should be the work of each individual student, using the text,
lecture material, and any other sources, besides any other student in the course. Any
indication that students worked together for the exam will result in both students receiving a
zero, which most likely lead to failing the course. Students shall submit the hand-written work
or excel sheets to show solution methods for each problem. All exams are to be emailed to the
instructor by midnight Monday April 30th.
Problem #1: (10 points – Graphical Solution Method)
Consider the linear programming problem:
Maximize: 𝑦 = 15𝑥1 + 15𝑥2
Subject to:
𝑥1 + 𝑥2 ≤ 1.5
𝑥1 + 2𝑥2 ≤ 2.1
𝑥1 , 𝑥2 ≥ 0
a). State whether the following values are feasible of non-feasible solutions:
Point (𝑥1 , 𝑥2 ), 1 (4, 10), 2 (6, 6), 3 (7, 2), 4 (8, 8)
b). Using the graphical solution method solve all corner points and find optimum point.
Problem #2: (30 Points – Integer LP Excel Solution)
Og is the leader of the surprisingly mathematically advanced, though technologically run-ofthe-mile, Calm Waters caveman tribe. He must decide on the number of stone clubs and stone
axes to be produced for an upcoming batte against the neighboring Peaceful Sunset tribe.
Experience has taught him that each club is good for, on average 0.45 kills and 0.65 maims,
while each axe produces 0.70 kills and 0.35 maims. Production of a club requires 5.1lb of stone
and 2.1 man-hours of labor, while an axe requires 3.2 lb of stone and 4.3 man-hours of labor.
Og’s tribe has 240 lb of stone available for weapon production, and a total of 200 man-hours of
labor. Og values a kill as worth two maims in quantifying the damage inflicted.
a). Define Decision Variables
b). Develop Objective Function
c). Define all constraints as described in the problem statement for both cases
d). Provide optimum solutions
CMGT_575_ Final_Exam
Problem #3: (25 points – Integer LP Excel Solution)
A company makes two types of products, A and B. These products are produced during a 40 hr
work week and then shipped out at the end of the week. They require 20 and 5 kg of raw
material per kg of product, respectively, and the company has access to 9,500 kg of raw
material per week. Only one product can be created at a time with production times of 0.04
and 0.12 hr, respectively. The plant can only store 550 kg of total product per week. Finally,
the company makes profits of $45 and $20 on each unit of A and B, respectively. Each unit of
production is equivalent to a kg.
a). Define Decision Variables
b). Develop Objective Function
c). Define all constraints as described in the problem statement
d). Provide optimum solution
Problem #4: (5 points – Inventory Control)
Determine the optimal inventory policy and associated cost per day. Assume that no shortage
is allowed and the lead time between placing and receiving an order is 30 days.
K = $100, h = $0.01, D = 40 units per day
Problem #5: (20 points – Project Mgmt)
The activities that constitute a project are listed. The project starts at t = 0.
Activity
predecessors
start
A
start
B
A
C
A
D
A
E
C
F
C
G
D, B
H
E, F
I
F, G
finish
H, I
a). Draw the critical path network
b). What is the earliest possible finish
c). What is the latest possible finish
successors
A
B, C, D
G
E, F
G
H
H, I
I
finish
finish
-
duration
0
7
6
5
2
13
4
18
7
5
0
CMGT_575_ Final_Exam
Problem #6: (10 points – Transportation Model)
The National Parks Service is receiving four bids for logging at three pine forests in Arkansas.
The three locations include 10,000, 20,000, and 30,000 acres. A single bidder can bid for at
most 50% of the total acreage available. The bids per acre at the three locations are given in
the table below. Bidder #2 does not wish to bid on location 1 and Bidder #3 can not bid on
location #2.
Bidder 1
Bidder 2
Bidder 3
Bidder 4
Site 1
$520
$650
$180
a). Formulate the associated transportation model
b). Determine the optimum shipping schedule
Site 2
$210
$510
$430
Site 3
$570
$495
$240
$710