ACCA F5《業(yè)績管理》經(jīng)典例題分析（上）

接下來我們學習一下考官給出的答案

Answer：

（a）第一步，先找出原材料Betta的缺口，即在滿足合約5000和市場需求2500的情況下有多少短缺。

經(jīng)過計算，三個產(chǎn)品對于Betta的總需求量15060，總供給12000，缺口是3060。

第二步， 計算單位貢獻，然后除以每個單位耗用Betta的情況，可以算出contribution per gram，根據(jù)其大小排序。

第三步，首先生產(chǎn)5000單位合約要求的產(chǎn)品，剩余的資源根據(jù)排序優(yōu)先生產(chǎn)9800個單位的cookies, 剩下的還能生產(chǎn)10080個單位cake。用產(chǎn)量乘以對應的單位貢獻得出總貢獻。

(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）問的前提是如果違約，是否可以先生產(chǎn)盈利性更強的產(chǎn)品。答案一定是不可以的。違約聲譽受影響，其他客戶會不信任公司，未來會有更多損失。而且違約還會帶來罰款，對企業(yè)來說也要承擔很大的成本。

(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問條件是公司失去了和健身房的合約，現(xiàn)在可以自主設計生產(chǎn)方案，但是原材料和人工都稀缺。在多種限制條件并存的情況下需要用線性規(guī)劃找到至優(yōu)解。設X為cake的產(chǎn)量，y為cookie的產(chǎn)量。

限制性條件如下：

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

每一條線代表每個不等式。

目標方程：C=2.6x+1.75y。

OABCD是可行性區(qū)域，找到目標方程和可行性區(qū)域離原點至遠的交點, 可以找到的contribution。

另外，本問中的slack value是個高頻考點。C的問題是在至優(yōu)生產(chǎn)方案下哪一種資源存在slack，也就是資源有閑置。本題至優(yōu)點是C（labor 和cake的交點），也就是說除了labor 和cake，原材料Betta和Singa都沒有被化的利用。另外Cookie的市場需求也沒有滿足，同樣存在slack value。

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