MBA8580: Business Analytics: Assignment 3

2/7/2021 MBA8580: Assignment 3
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MBA8580: Business Analytics: Assignment 3
This assignment is designed to introduce you to linear programming, integer programming and optimizationmodeling. Please read through all instructions for the assignment as they pertain to modeling issues withSolver.
Instructions
1.
Place all of the following problems in one Excel file on separate sheets (one sheet for each problem).
2.
Submit only your team’s final model for each problem.
3.
Make sure that the solver dialogue box contains all the information for your model.
4.
Make sure to answer all questions that are asked.
5.
On the first sheet, put the names of all group members as well as all explanations for all of theproblems.
6.
Name the file with at least one group member’s name in the filename.
7.
Please do not zip your files.
See course schedule for due dates.
Problem 1
A􀁸er completing this course, you enroll in the data mining elective course which has one exam, a project,individual assignments, and class participation. Your scores on these grade components are shown below.
Scores
Component
Score
Exam
86
Project
94
Assignments
93
Participation
85
The instructor has allowed you to determine your own weights for each of the four grade components withthe following restrictions:
the participation score can be weighted no more than 15% of the total
exam must count at least twice as much as the individual assignment score
project must count no more than three times the individual assignment score
each of the four components must count for at least 10% of the course grade
2/7/2021 MBA8580: Assignment 3
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the weights must sum to 1.0 and be nonnegative
Use Solver to determine a valid set of weights to maximize your grade for the course.
Problem 2
During the next six weeks, a company faces the following demands:
Company Data
Week
1
2
3
4
5
6
Demand
600
800
1000
700
800
400
Unit production costs in weeks 1-6 are: $50, $80, $50, $70, $75, and $70 respectively. The storage cost fromone week to the next is $30 per unit (assessed on ending inventory). At the beginning of week 1 the companyhas 500 units on hand. Unfortunately, its production process is such that there is a 50% yield (i.e., only 50% ofthe units it produces in any week are of su􀁷icient quality to be used to meet demand). The remainder isdiscarded. All demand must be met each week.
a.
Determine how to minimize the cost of meeting demand over the next six weeks.
b.
Use SolverTable to determine how the optimal production quantities over the next six weeks vary asthe production yield increases from 50% to 90% (in 5% unit increments).
Problem 3
The so􀁸ware support division of GE has ten projects that can be performed. Each project requires di􀁷erentamounts of development time and testing time. In the coming planning period 700 hours of developmenttime and 600 hours of testing time are available and no more than five projects can be selected. Due to somecommon resources the company cannot work on both projects 5 and 7 together in the planning period. Also,if GE chooses to take on project 6 it must also undertake project 10 and vice versa. The projected revenue andtime required for each project are shown below. The table also indicates the fixed cost associated withundertaking each of the projects. Which projects should be selected to maximize profit?
GE Data
Project
Development
Time (hr)
Testing
Time (hr)
Revenue
Fixed Cost
1
80
67
$23,000
$5,000
2
295
208
$64,000
$7,000
3
32
19
$12,000
$1,500
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Project
Development
Time (hr)
Testing
Time (hr)
Revenue
Fixed Cost
4
26
92
$32,000
$6,000
5
240
202
$71,000
$8,000
6
195
164
$57,000
$7,500
7
205
226
$69,000
$8,000
8
110
92
$32,000
$2,000
9
129
44
$31,000
$3,000
10
97
52
$18,000
$2,000
Problem 4
Harry & David’s Co. buys oranges and processes them into gi􀁸 fruit baskets and fresh juice. The companygrades the fruit it buys on a scale from 1 (lowest quality) to 5 (highest quality). The following tablesummarizes the company’s current inventory level of fruit.
Fruit
Grade
1
2
3
4
5
Supply (1000’s of lbs)
172
288
415
333
92
Each pound of oranges devoted to fruit baskets results in a marginal profit of $2.50, whereas each pounddevoted to fresh juice results in a marginal profit of $1.75. The company wants the fruit in its baskets to havean average quality grade of at least 3.75 and its fresh juice to have an average quality grade of at least 2.50.
Use Solver to determine
how many oranges of each grade should be used in fruit baskets and fresh juice
to maximize Harry & David’s profit.
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