Analysis of Wage Rate, Production, and Profit Maximization Strategies

This project encompasses two primary scenarios: wage rate analysis and production optimization. The first scenario investigates the impact of wage rate changes on production costs using simple aggregate and average wage rate relative indices. It then delves into Laspeyre and Paasche wage rate indices to assess the financial implications of increased labor costs, concluding that a wage increase is justified for worker satisfaction. The second scenario explores a perfume production company, 'Perfect Aroma,' utilizing linear programming to maximize profit. It defines an objective function, constraints, and extreme points to determine optimal production levels of two perfume types, Bushido and Hansei. The project also analyzes the impact of unused resources and evaluates an offer from an American firm. Finally, it assesses the impact of limited solution availability on production and profit, recalculating optimal production levels under new constraints.

Indices/ Linear Programming

Contents
SCENERIO 1: Production staff wage rate analysis.........................................................................1
Task 1...........................................................................................................................................1
Task 2...........................................................................................................................................2
Task 3...........................................................................................................................................3
SCENERIO 2: Perfect Aroma.........................................................................................................4
Task 1...........................................................................................................................................4
Task 2...........................................................................................................................................6
Task 3...........................................................................................................................................6
Task 4...........................................................................................................................................6

SCENERIO 1: Production staff wage rate analysis
Task 1
A local manufacturing organisation is considering to increase the pay of their labourers for
which this company requires to understand how much production cost have been increased in
last 2 years. For this purpose, two methods of calculating price index are used below from which
different results are gathered.
Simple aggregate wage rate index - This method considers index number as the sum of
prices or rates of a year divided by sum of prices or rates of the base year. Hourly wage rate for 2
years that is 2017 and 2019 is provided in which year 2017 will be considered as a base year.
Formula - P01 = (Sum of P1 / Sum of P0) * 100
In this P0 is the sum of prices of base year, P1 is sum of prices of the year for which index number
is required to be calculated and P01 is the index number.
Commodity Prices in 2017 (Base year) (P0) Prices in 2019 (Current year)
(P1)
1 8.26 8.90
2 8.88 9.67
3 10.14 10.17
4 10.83 11.46
5 11.74 12.20
Total 49.85 52.4
P01 = (52.4/49.85) * 100
= 105.11
Average wage rate relative index – This method is slightly different from above method
as in this index number is considered to be as the sum of price relatives divided by the total of
items.
Formula - P01 = Sum of R / N
In above formula R is sum of price relatives which can be calculated by dividing prices of
current year and base year * 100, N is number of items and P01 is index number.
Commodity Prices in 2017 (Base year) Prices in 2019 (Current year) Price relatives
1

(P0) (P1) P1 / P0 * 100
1 8.26 8.90 107.75
2 8.88 9.67 108.90
3 10.14 10.17 100.30
4 10.83 11.46 105.82
5 11.74 12.20 103.92
N = 4 526.68
P01 = Sum of R / N
P01 = 526.68 / 4
= 131.67
The price index which calculated from simple aggregate wage rate index is 105.11 and
the price rate calculated from average wage rate relative index is 131.67. The price indices in
both the cases are different. This difference is the result to different implementation approach as
in one method all the prices are sum together but in second method an average is calculated of all
the prices. By analysing the scenario, it can be said that both of these methods are not suitable for
this situation. As it has observed that there are 5 grades of labourers in manufacturing company
and calculating a price index without understanding the importance or weight of each labour
grade is irrelevant.
Task 2
Laspeyre wage rate indices
Formula – P01 = Sum of P1q0 / Sum of P0q0 * 100
Commodities 2017 (Base year) 2019 (Current year) P0q0 P1q0
Price (P0) Weights (q0) Price (P1) Weights (q1)
1 8.26 18 8.9 16 148.68 160.2
2 8.88 40 9.67 45 355.2 386.8
3 10.14 16 10.17 12 162.24 162.72
4 10.83 14 11.46 10 151.62 160.44
5 11.74 32 12.2 35 375.68 390.4
Total 1193.42 1260.56
2

P01 = 1260.56 / 1193.42 * 100
P01 = 105.62
Paasche wage rate indices
Formula – P01 = Sum of P1q1 / Sum of P0q1 * 100
Commodities 2017 (Base year) 2019 (Current year) P0q1 P1q1
Price (P0) Weights (q0) Price (P1) Weights (q1)
1 8.26 18 8.9 16 132.16 142.4
2 8.88 40 9.67 45 399.6 435.15
3 10.14 16 10.17 12 121.68 122.04
4 10.83 14 11.46 10 108.3 114.6
5 11.74 32 12.2 35 410.9 427
Total 1172.64 1241.19
P01 = 1241.19 / 1172.64 * 100
P01 = 105.84
From the above Laspeyre and Paasche wage rate methods, it has been seen that price
index has been increased to an average of 105. Analysing this price index, it can be said that the
manufacturing company has to pay additional value of 105 against their production costs. In this
situation, it is not viable to increase the pay of labourers. But this price index rise impacts
expenses of workers as well due to which they will be satisfied only when they will have
increase wage pay. Analysing both the aspects, it has been concluded that manufacturing
company should increase pay of their labourers so that they can acquire satisfaction.
Task 3
While acquiring the externals data, there are various factors which must be considered so
that comparison between wage rate of government averages and manufacturing company can be
accurate. These factors include similar base year, same number of grades of labour and similar
procedure of assigning weights.
SCENERIO 2: Perfect Aroma
Task 1
Solution A Solution B Solution C Profit
3

Bushido 96 4 30 12
Hansei 80 6 60 16
Availability of solutions 48000 2400 22500
Objective function Maximum Z=12X+16Y
Constraints: 96X+80Y≤48000 12X+10Y≤6000
4X+6Y≤2400 2X+3Y≤1200
30X+60Y≤22500 1X+2Y≤750
Non-negativity restriction X ≥ 0 & Y ≥ 0 X ≥ 0
Y ≥ 0
C1
X Y
0 600
500 0
C2
X Y
0 400
600 0
C3
X Y
0 375
750 0
Extreme Point Lines through Extreme
Point
Objective function value
Coordinates z=12x1+16x2
(x1,x2)
4

O(0,0) 4→x1≥0 12(0)+16(0)=0
5→x2≥0
A(500,0) 1→12x1+10x2≤6000 12(500)+16(0)=6000
5→x2≥0
B(375,150) 1→12x1+10x2≤6000 12(375)+16(150)=6900
2→2x1+3x2≤1200
C(150,300) 2→2x1+3x2≤1200 12(150)+16(300)=6600
3→x1+2x2≤750
D(0,375) 3→x1+2x2≤750 12(0)+16(375)=6000
4→x1≥0
Extreme point which is observed above is B (375, 150)
So, Z = 12X+16Y
Z = 12*375 + 16*150
Z = 4500 + 2400 = 6900
Number of Bushido to be produced to acquire maximum profit = 375
Number of Hansei to be produced to acquire maximum profit = 150
5

Task 2
Bottles to be
produced
Required
Solution A
Required
Solution B
Required
Solution C
Bushido 375 36000 1500 11250
Hansei 150 12000 900 9000
Sum 48000 2400 20250
Availability of
solutions 48000 2400 22500
Unused resources 0 0 2250
2250 ml of solution C will be remained unused which can enhance production cost of the
company.
Task 3
In the given scenario, Perfect Aroma has been given an opportunity by American firm
which is willing to buy 300 bottles of Bushido every month for next 6 months. According to the
computations done in above sections, this offer should be accepted by the Perfect Aroma. This
statement is based on the observation that this company requires to produce 375 bottles every
month to acquire maximum profit. By selling 300 bottles of American company individually, the
maximum profit can be easily acquired by this company. This company have to consider that
there is continuous supply of solutions A, B and C so that production process can run smoothly.
Task 4
In the scenario, where supply of solution C will be limited to 1800 ml, a deficit will rise for
this solution of 2250 ml.
Solution A Solution B Solution C Profit
Bushido 96 4 30 12
Hansei 80 6 60 16
Availability of solutions 48000 2400 18000
objective function Maximum Z=12X+16Y
constraints: 96X+80Y≤48000 12X+10Y≤6000
4X+6Y≤2400 2X+3Y≤1200
6

30X+60Y≤18000 1X+2Y≤600
non-negativity
restriction X ≥ 0 & Y ≥ 0 X ≥ 0
Y ≥ 0
X Y
Z 12 16
C1 12 10 ≤ 6000
C2 2 3 ≤ 1200
C3 1 2 ≤ 600
C1
X Y
0 600
500 0
C2
X Y
0 400
600 0
C3
X Y
0 300
600 0
Extreme Point Lines through Extreme
Point
Objective function value
Coordinates z=12x1+16x2
7

(x1,x2)
O(0,0) 4→x1≥0 12(0)+16(0)=0
5→x2≥0
A(500,0) 1→12x1+10x2≤6000 12(500)+16(0)=6000
5→x2≥0
B(428.57,85.71) 1→12x1+10x2≤6000 12(428.57)+16(85.71)=6514.29
3→x1+2x2≤600
C(0,300) 3→x1+2x2≤600 12(0)+16(300)=4800
4→x1≥0
Extreme point which is observed above is B (428.57,85.71)
So, Z = 12X+16Y
Z = 12*428.57+ 16*85.71
Z = 6521.29
Due to this scenario,
Number of Bushido to be produced = 428.57
Number of Hansei to be produced = 85.71
And the Profit will be 6521.29
8