Question 1 Xv => Maximum No. Of vacuum cleaners to be produced
Xw => Maximum No. Of washing machines to be produced
Linear Program Objective Function
Max Profit => $800 Xv + $1,200 Xw
Constraints
Labour Days
20 Xv + 50 Xw = 3,000
Material
$1,000 Xv + $ 1,500 Xw = $250,000
Variables and Constraints
Vacuum Cleaner (Xv)
Washing Machine (Xw)
Maximum Availability
Labour Days
20
50
3000
Material
$ 1,000
$ 1,500
$ 250,000
Profit
$ 800
$ 1,200
Original Problem
Maximize
X1
X2
Labour Days
20
50
<=
3000
Material
$ 1,000.00 $ 1,500.00 <=
$ 250,000.00
Condition 1
1
0
>=
50
Condition 2
0
1
>=
20
Dual Problem
Labour Days
Material
Condition 1
Condition 2
Minimize
3000
$ 250,000.00
-50
-20
X1
20
$ 1,000.00
-1
0
>=
$ 800.00
X2
50
$ 1,500.00
0
-1
>=
$ 1,200.00
X1
X2
RHS
Dual
Maximize
$ 800.00 $ 1,200.00
Labour Days
20
50
<=
3000
40
Material
$ 1,000.00 $ 1,500.00
<=
$ 250,000.00 $ -
Condition 1
1
0
>=
50
0
Condition 2
0
1
>=
20
-800
Solution->
100 units
20 units
104000
Productivity Level
Vacuum Cleaners
Washing machine
Maximum Profitability
At Max Washing Machines
50
40
$ 88,000
At Maximum Vacuum Cleaners (Optimal Level)
100
20
$ 104,000
At Minimum
50
20
$ 64,000
Thus:
At optimal Level i.e. Xv => 100 and Xw => 20
Linear Program Objective Function
Max Profit => $ 800 (100) + $1,200 (20)
Max Profit => $ 80,000 + $ 24,000
Max Profit => $ 104,000
Constraints
Labour Days
20 (100) + 50 (20) = 3,000
2,000 + 1,000 < 3,000
Material
$1,000 (100) + $ 1,500 (20) = $250,000
$ 100,000 + $ 30,000 < $ 25,000
On the basis of above solution, we can see that the optimal solution for producing Vacuum Cleaner and Washing Machine is 100 and 20 units respectively as the number of days and Material cost are restricted. So the optimal level of production is 100 Vacuum Cleaner and 20 Washing Machine with maximum profitability of $ 104,000.
Question 2
Characteristics of an Effective Performance Measurement System
There are six basic characteristics of an effective performance measurement system, even though we support the performance management plan to be tailored in accordance with the organizational culture and business strategy, but the six characteristics should be the cornerstone of all performance management system.
1.The continuing system of planning, directing, evaluating and rewarding performance management to establish and consolidate all the four pillars of the personnel management process is still planning, training, review and reward (Murby, L., & Gould, S., 2005, p.5-11). Weakened in any one of them, the entire system will be damaged.
2.Performance management is linked with specific business objectives; you need to push down from high and link the goals with business strategy in order to solve the plight of performance measurement and clearly communicate with employees, so that employees are able to understand their goals with necessary organizational goals.
3.Performance indicators are built on the basis of quantifiable targets and capacity. Until recently, most organizations can only rely on a separate market share, profit and operating income of this digital navigation (Salem, 2004, p.1-20).
4.Performance measurement is the obligation of managers at all levels, and managers at all levels must take the initiative to participate in the performance management. People generally believe that performance measurement is a matter of the human resources department, rather than a matter of department managers.
5.Performance measurement must be linked with other systems, must be clear with employees to communicate salary. When the company changed its pay system, it will convey two messages to employees: ...