4 Limiting factor analysis

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1 4 Limiting factor analysis
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2 1 2 3 4 5 Limiting factors The principle of linear programming
The graphical method 4 Slack and surplus 5 Shadow price

3 Limiting factors All companies have a maximum capacity for producing goods or providing services , because there is a limit to the amount of resources available . There is always at least one resource that is more restrictive than others : this is known as a limiting factor. A limiting factor is any factor that is in scarce supply and that stops the organisation from expanding its activities further , so that there is a maximum level of activity at which the organisation can operate.

4 Resource limiting factor
Limiting factors Limiting factor analysis that management will decide to use its scarce resources in such a way as to maximise total contribution . Marginal cost ideas are applied. Max contribution Earning the biggest possible contribution per unit of limiting factor Resource limiting factor

5 1.Identify limiting factor
Limiting factors Step: 1.Identify limiting factor 2.Calculate contribution per limiting factor 3.Rank products 4.Prepare a budget production plan

6 The principle of linear programming
Linear programming is a technique for solving problems of profit maximisation or cost minimisation and resourse allocation. If contains two or more limiting fators,linear programming can be used to determine the contribution -maximising or cost-minimising solution. When an organisation makes and sells just two products, a graphical method can be used to formulate the linear progr- amming problem and then solve it.

7 The graphical method The steps involved are as follows:
1.Define variables 2.Establish constraints 3.Construct objective function 4.Graph constraints 5.Establish the feasible region 6.Add iso-profit/contribution line 7.Determine the optimal solution 2019/4/23

8 Example for calculation
BLtd makes just two modles,the Super and Deluxe, and that the only constraint faced by the company iss that monthly machine capacity is restricted to 400 hours.The Super requires 5 hours of machine time per unit and the Deluxe 1.5 hours.Goverment restrictions mean that the maximum number of units that can be sold each month is 150,that number being made up of any combination of the Super and the Deluxe. And the profit per unit is $100 on Super $200 on Deluxe. 2019/4/23

9 let x=the production units of Super and y for Deluxe
1.Define variables 定义变量 let x=the production units of Super and y for Deluxe 2.Establish constraints 确定约束条件 5x+1.5y≤400 ; x+y≤150 ; x≥0 ; y≥0 3.Construct objective function 建立目标函数 P=100x+200y 2019/4/23

10 4.Graph constraints 将约束条件图形化 5.Establish the feasible region 确定适合区域
6.Add iso-profit/contribution line画出等利润线 7.Determine the optimal solution 找出最优解 Optimal solution is: 5x+1.5y ≤ Super 0 x+y ≤ Deluxe 150 x ≥0 ,y ≥0 P=100x+200y 2019/4/23

11 Some question should be discussed
Multiple solutions 多个解得问题 This will occur when the profit line is exactly parallel to one of the constraint lines. Minimization problems 最小化问题 Minimize costs 方法同利润最大化 The graphical method using simultancous equation 以联立方程simultancous equation 求解是通用方法，结合联立方程的图解法 2019/4/23

12 Slack and Surplus When maximum availability of a resource is not used, slack occurs. When more than a minimum requirement is used, surplus occurs.

13 Shadow Price The price or dual price is the extra contribution or profit that may be created by having one additional unit of the limiting factor at the original cost.

14 Shadow price Shadow Price影子价格影子定价就是指基金管理人于每一计价日，采用市场利率和交易价格，对基金持有的计价对象进行重新评估，即“影子定价”。 当基金资产净值与影子定价的偏离达到或超过基金资产净值的0.5%时，或基金管理人认为发生了其他的重大偏离时，基金管理人可以与基金托管人商定后进行调整，使基金资产净值更能公允地反映基金资产价值，确保以摊余成本法计算的基金资产净值不会对基金持有人造成实质性的损害。 影子定价的作用在于为了避免采用摊余成本法计算的基金资产净值与按市场利率和交易市价计算的基金资产净值发生重大偏离，从而对基金持有人的利益产生稀释和不公平的结果。

15 Key Points If a constraint is not binding at the
optimal solution ,the shadow price is zero. The shadow price represents the maximum premium above the basic rate that an organization should be willing to pay for one extra unit of a resource. Key Points Shadow are only valid for a small range. Shadow price provide a measure of the sensitivity of the effect of a unit change in a constraint.

16 Thank you