M8A1 Project: Detailed Analysis of Optimal Business Solutions

This project presents an analysis of optimal solutions for a business, addressing key aspects such as cost optimization, budget allocation, and employee office allocation. The first section focuses on minimizing the cost of copper inputs across multiple plants, identifying the total cost, and analyzing binding and non-binding constraints, including a shadow price analysis. The second section delves into budget allocation, presenting the best projects to undertake based on costs, returns, and engineer requirements. The final section addresses employee office allocation, considering both preference-based and seniority-based allocation strategies. The project provides detailed tables and analyses to support the findings, offering insights into efficient resource management and decision-making within a business context.

M8A1 Assignment
Student name
Date

1. Fasts optimal solution
a) Cost of the optimal mix
The table below gives a summary of the amounts of copper in tones that Fast bought
from each of the company’s to be supplied to each of the plants.
Amounts of copper to buy (tons)
Company 1 Company 2 Company 3 Company 4 Company 5
Total
Bought for
each plant
Plant
Demand
Plant 1 0 192 148 0 90 430 430
Plant 2 0 0 50 300 0 350 350
Plant 3 0 0 0 0 400 400 400
Plant 4 300 58 12 0 0 370 370
Total Purchased from each company 300 250 210 300 490
Available supply 350 250 210 300 490
Cost of Copper $15,000 $11,750 $10,080 $13,500 $21,070 $71,400
Cost of shipping $2,400 $1,000 $950 $600 $1,160 $6,110
Total cost $77,510
From the table the cost of the copper inputs is $ 71,400 while that of shipping is $
6110. The total cost of the optimal mix is thus $ 77,510.
b) Answer report analysis
The table presents a section of the answer report for the binding and non-binding
constraints.
Constraints
Cell Name Cell Value Formula Status Slack
$B$22 Total Purchased from each company Company 1 300 $B$22<=$B$23 Not Binding 50
$C$22 Total Purchased from each company Company 2 250 $C$22<=$C$23 Binding 0
$D$22 Total Purchased from each company Company 3 210 $D$22<=$D$23 Binding 0
$E$22 Total Purchased from each company Company 4 300 $E$22<=$E$23 Binding 0
$F$22 Total Purchased from each company Company 5 490 $F$22<=$F$23 Binding 0
$G$18 Plant 1 Total Bought for each plant 430 $G$18=$H$18 Binding 0
$G$19 Plant 2 Total Bought for each plant 350 $G$19=$H$19 Binding 0
$G$20 Plant 3 Total Bought for each plant 400 $G$20=$H$20 Binding 0
$G$21 Plant 4 Total Bought for each plant 370 $G$21=$H$21 Binding 0
The report has one non-binding constraint. The non-binding constraint is the quantity
purchased from company 1 to be shipped to either plant 1,2,3 or 4. The amount of
slack arising from the non-binding constraint is 50 tons of copper.
c) Shadow price

A shadow price of -7 for Total company 2 means that should the purchase from
company 2 to either of the plants ne increased by a 1 ton, then the objective function
that is the total cost will be reduces by $ 7. This effect means that should the
maximum copper obtained from company 2 increase then the objective function will
be optimized.
2. Budget allocation
The table below summarizes the best projects to be undertaken by the company.
Project type Additional cost
($)
Engineers Return ($)
1 190,000 8 600,000
3 370,000 7 750,000
5 225,000 8 350,000
6 275,000 10 725,000
Total 1,060,000 33 2,425,000
This consumes a total of $ 1060000 in costs while at the same time yielding a return of
$2425000. A total of 33 engineers will be engaged in the 4 projects.
3. Settling employees in the new offices
a) The office allocation for the employees are summarized by the table below with the
preference attached.
Employee Office allocated Preference
1 6 5
2 7 9
3 5 7
4 1 7
5 7 9
6 9 10
7 4 9
8 10 10

9 2 9
10 8 7
11 8 10
12 5 10
13 3 10
14 9 8
120
b) Allocation of the offices based on seniority
Employee Office allocated Preference
1 7 8
2 8 8
3 5 7
4 6 4
5 7 9
6 1 4
7 4 9
8 2 5
9 5 4
10 8 7
11 9 4
12 9 7
13 10 7
14 3 5
88
From the output of the solver, the total preference the employees reduce when their
seniority is put into account during office room allocation