Management Science in Statistics

This document discusses the application of management science in statistics, specifically in formulating linear programming (LP) problems and solving them using Excel solver. It covers topics such as production problem, investment decision problem, and media selection problem. The document provides step-by-step instructions, constraints, and objective functions for each problem, as well as the optimal solutions obtained using Excel solver. Recommendations are also given based on the results.

Running head: MANAGEMENT SCIENCE IN STATISTICS
1
Management Science in Statistics
Student Name
Institution Affiliation

MANAGEMENT SCIENCE IN STATISTICS
2
1. Production Problem
a. Formulate as an LP problem.
Let X to be the French provincial model manufactured.
Let Y to be the Danish modern model manufactured.
The objective function will be to maximize Z=28X+25Y
Subject to constraints; X+Y≥60
; 3X+2Y≥360
;3X+2Y≥400
;3X+3Y≥500
Trivial constraints X,Y≥0
b. Solve this problem using Excel solver.
See attached excel sheet for solver.
i. What would you suggest to Bob Winkler to solve this problem?
The main objective of business entities is to maximize revenues while maintaining
minimal costs, in the process of production, Krajewski et al (2013) suggested that
firms should shift their focus to production and management practices that
enhance their competitive advantage. Using the excel solver the optimal solution
to maximize the daily revenue is to produce the French provisional model at
26.667 cabinet per week and 140 Danish modern model cabinet per week. The
algorithm applied is the simple method proposed by (Kolotilin, 2018)

MANAGEMENT SCIENCE IN STATISTICS
3
c. If the available painting hours are increased to 400 hours, will your answer in (b)
change?
If the painting hours are increased to 400 hours then the optimal solution will be
affected and will change.
2. Investment decision problem
a. Formulate as an LP problem
Let B to be the municipal bonds
Let C to be aerospace firms, electronic firms, and manufacturers of drugs.
Let D to be the high risk account
Objective: Maximize the projected returns;
Max Z = 0.053B + 0.201C + 0.118D
Constraints ; B+C+D≤250000
B≥5000
C≥10000
D≤2500
Trivial constraints B, C,D≥0
b. Solve this problem using Excel solver. See attached excel sheet for solver.
i. What would you suggest to the client?
The optimal solution from the excel solver the client should be advised to
invest 5000 on municipal bonds, 245000 on the combination of
electronics, aerosol and drug manufacturing and not to invest in the high
risk account of the nursing homes care (Fletcher, 2013).
c. If the projected rate of return of “Happy Days Nursing Homes” drops to
6.0% next year, would you suggest the client to invest it? Please explain
based on your new findings using Excel solver?

MANAGEMENT SCIENCE IN STATISTICS
4
If the nursing homes projected returns drop to 6% in the projected next year then the
client will be advised to maintain the investment as it is in the first case since the
nursing home was not selected in the first case.
3. Media selection problem
a. Formulate as an LP problem
The decision of choice will either to use half page ads or the TV adverts.
Let X be the use of the half page ads
Let Y be the TV adverts
The problem falls under the minimization of cost on the two decision and the least
cost will be the optimal solution.
The objective function is Min Z =2000Y + 925X
Subject to ; 0.05Y + 0.04X ≥0.4
0.03Y + 0.03X≥0.6
Trivial constraints Y, X ≥0
b. Solve this problem using Excel solver. See attached excel sheet for solver.
i. What would you suggest to Diversey Paints?
The optimal solution from the excel solver will be to advise the Diversey paints to use
the half page tribune adverts rather than the TV advert. Diversey paints should indeed
use purely half page ads at rate of 20 and 0 TV ad to minimize cost. The best set of
combination was achieved using the optimality conditions as stated by (Andrei,
2017).

MANAGEMENT SCIENCE IN STATISTICS
5
c. Comparing between the 2 methods of publication the TV advert should be the
most effective method .this is due to facts that it can capture a wider audience in a
faster way.

MANAGEMENT SCIENCE IN STATISTICS
6
References
Andrei, N. (2017). Active-set Sequential Linear-Quadratic Programming:
KNITRO/ACTIVE. In Continuous Nonlinear Optimization for Engineering
Applications in GAMS Technology (pp. 305-315). Springer, Cham.
Fletcher, R. (2013). Practical methods of optimization. John Wiley & Sons
Kolotilin, A. (2018). Optimal information disclosure: A linear programming
approach. Theoretical Economics, 13(2), 607-635.
Krajewski, L. J., Ritzman, L. P., & Malhotra, M. K. (2013). Operations management.
Pearson,.