Math Modeling and Decision Analysis | Assessment

Math Modeling and Decision Analysis
Student Name:
Instructor Name:
Course Number:
6th October 2019

Problem:
The problem here is about a large Chain Store supermarket that plans to open up a maximum of
15 new stores in a new city that management has identified. The stores needs to be built in one of
three sizes for every location – Store A (operates 24 hours), Store B (operates normal hours) and
Store C (operates till late hours). Store A requires 4.565 million dollars to construct and about 25
employees to operate. Store B requires 9.35 million dollars to construct and 12 employees to
operate. Store C requires 13.455 million dollars to construct and 50 employees to operate. The
Chain store can put aside 88.375 million to go towards the construction, 450 employees to
operate in the stores. On average, it is believed that Store A would net approximately 1.5 million
dollars every year, Store B would net 2.85 million dollars every year and Store C would net 3.15
million dollars every year. We need to find the number of each stores that need to construct so as
to maximize on their revenues.
Solution
This problem is a linear programming and optimization problem that might pose a great risk to
the business. Failure to construct the number of units based on the optimal consideration might
result to a risk of losing money hence failing to make profits as would be required by the
management. It is therefore essential to obtain the optimal values of the number of units that
need to constructed that would result in the Chain Store making or rather maximizing on their
profits/revenues.
To solve this problem, we start by assigning the variables as follows;
Let:
x1=Store A

x2=Store B
x3=Store C
We write the constraints as follows;
x1+ x2 + x3 ≤ 15
4.65 x1 +9.35 x2+13.455 x3 ≤ 88.375
25 x1+12 x2+50 x3 ≤ 4 5 0
x1 ≥ 0 ; x2 ≥ 0∧x3 ≥0
The objective function is:
N ( x1 , x2 , x3 )=1.5 x1+ 2.85 x2 +3.15 x3
This problem is solved using excel’ s solver
Results
From the excel solver, we obtained the following results;
Answer Report
Microsoft Excel 16.0 Answer Report
Worksheet:
[Book4]Sheet1
Report Created: 10/6/2019 3:22:25 PM
Result: Solver found a solution. All Constraints and optimality
conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.062 Seconds.
Iterations: 3 Subproblems:
0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001