ACCA F5《业绩管理》经典例题分析（下<答案>）

ACCA F5《业绩管理》经典例题分析（上）

接下来我们学习一下考官给出的答案

Answer：

（a）第一步，先找出原材料Betta的缺口，即在满足合约5000和市场需求2500的情况下有多少短缺。

经过计算，三个产品对于Betta的总需求量15060，总供给12000，缺口是3060。

第二步， 计算单位贡献，然后除以每个单位耗用Betta的情况，可以算出contribution per gram，根据其大小排序。

第三步，首先生产5000单位合约要求的产品，剩余的资源根据排序优先生产9800个单位的cookies, 剩下的还能生产10080个单位cake。用产量乘以对应的单位贡献得出总贡献。

(b) Breach of contract with Encompass Health (EH)

It would be bad for business if CSC Co becomes known as a supplier who cannot be relied on to stick to the terms of its agreements. This could make future potential customers reticent to deal with them.

Even more seriously, there could be legal consequences involved in breaching the contract with EH. This would be costly and also very damaging to CSC Co’s reputation.

If CSC Co lets EH down and breaches the contract, EH may refuse to buy from them any more and future sales revenue would therefore be lost. Just as importantly, these sales to EH are currently helping to increase the marketability of CSC Co’s shakes.

This will be lost if these sales are no longer made.

Therefore, taking these factors into account, it would not be advisable to breach the contract.

（b）问的前提是如果违约，是否可以先生产盈利性更强的产品。答案一定是不可以的。违约声誉受影响，其他客户会不信任公司，未来会有更多损失。而且违约还会带来罚款，对企业来说也要承担很大的成本。

(c) (i) This line is what is called the ‘iso-contribution line’ and it is plotted by finding two corresponding x and y values for the ‘objective function’. At any point along this line, the mix of cakes and cookies will provide the same total contribution, ‘C’.

Since each cake provides a contribution of $2·60 and each cookie provides a contribution of $1·75, the objective function has been defined as ‘C = 2·6x + 1·75y’. This means that the total contribution will be however many cakes are made (represented by ‘x’) at $2·60 each plus however many cookies are made (represented by ‘y’) at $1·75 each.

The area 0ABCD is called the ‘feasible region’. Any point within this region could be selected and would show a feasible mix of production of cakes and cookies. However, in order to maximise profit, the optimum production mix will be at a point on the edge of the feasible region, not within it.

(ii) The further the iso-contribution line is moved away from the origin, 0, the greater the contribution generated will be.

Therefore, a ruler will be laid along the line, making sure it stays at exactly the same angle as the line, and the ruler will then be moved outwards to the furthest vertex (intersection between two constraints) on the feasible region, as represented by either point A, B, C or D. In this case, the optimum point is ‘C’, the intersection of the ‘labour’ constraint and the ‘demand for cakes’ constraint.

(iii) A ‘slack’ value could arise either in relation to a resource or in relation to production of a product. It means that a resource is not being fully utilised or that there is unfulfilled demand of a product. Since the optimum point is the intersection of the labour and the demand for cakes lines, this means that there will be three slack values. First, there will be a slack value for cookies. This means that there will be unsatisfied demand for cookies since the optimum point does not reach as far as the ‘demand for cookies’ line on the graph. Also, there will be slack values for Betta and Singa, which means that both of these materials are not actually the binding constraints, such that there will be more material available than

is needed.

c问条件是公司失去了和健身房的合约，现在可以自主设计生产方案，但是原材料和人工都稀缺。在多种限制条件并存的情况下需要用线性规划找到至优解。设X为cake的产量，y为cookie的产量。

限制性条件如下：

Singa: 0·25x + 0·5y ≤ 12,000

Betta: 0·5x + 0·2y <=  12,500

Labour: 0·1x + 0·12y <=  3,000

x  <=  20,000

y  <=  15,000

x, y  >=   0

每一条线代表每个不等式。

目标方程：C=2.6x+1.75y。

OABCD是可行性区域，找到目标方程和可行性区域离原点至远的交点, 可以找到的contribution。

另外，本问中的slack value是个高频考点。C的问题是在至优生产方案下哪一种资源存在slack，也就是资源有闲置。本题至优点是C（labor 和cake的交点），也就是说除了labor 和cake，原材料Betta和Singa都没有被化的利用。另外Cookie的市场需求也没有满足，同样存在slack value。

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