Linear Programming

The statement to show the maximum profit achievable for February 2005

Product (012) 1,000 units x £35 = £35,000

Product (036) 1,500 units x £20 = £30,000

Product (048) 2,000 units x £10 = £20,000

Product (060) 1,750 units x £15 = £26,250

       £111,250

Less Fixed Costs                        (£70,000)

    Profit / (Loss)                             £41,250

• Above is the profit statement for Mirabeau Ltd if they were to produce their goods according to the assumptions I have made above, then the company should still make a substantial profit.

From looking at all the information above it is clear to see that Mirabeau Ltd will have to look at all their products and produce the goods in order of which product gives out the highest contribution. So then the company will make use of the material shortage, starting with the product that gives out the highest contribution. This way the company will make use of the 16,000ml and still maximise profits. So in this case the company will produce all of product (012) 2,000ml as it gives out the highest contribution. Secondly they will produce all of product (036) 3,000ml; thirdly Mirabeau Ltd will produce all of product (048) 4,000ml then finally the company can only produce 1750 units of product (060) 7,000ml and then Mirabeau Ltd will utilise all of the available 16,000ml of materials.

Then however the company will have to decide what to do with the remainder of product (060) and also what they will do about product (024) which did not give out any contribution. This will be discussed later on in this report.

3.0 The assumptions and limitations 

The first assumption we can take into consideration is that the fixed costs remain constant throughout all levels of output. A limitation to this may be that in a realistic situation this may not always true as fixed costs are likely to change at different levels of output, for example if the company decide to increase their production levels.

Another assumption may be that the variable costs of the products remain constant for all levels of activity. This assumption is too simplistic in contrast with a realistic situation, as you would have to take into account things like overtime where extra hours worked will affect the variable cost of production and therefore have a knock on affect on the decision made by the management.

A further assumption may be that it is assumed that demand for the product will remain the same for all levels of output. If you take an economical point of view there are many factors which may have an affect on the demand of a product. For example things like price, location, weather or even if there is a substitute product brought in by the company. So if any of these factors have an affect on the goods then they will also have an impact on demand for any particular product. This may therefore lead to a financial crisis and the management will make a decision without really considering the effects of the economy.

Another assumption may be that we assumed that production will run smoothly throughout to meet the required demand. This assumption may be deemed to be too theoretical. This is because if you look at this in a more realistic way it is very likely that production may get stopped at some time during the process which will also have an affect on the whole production line. This will also be important for the management when making a decision on what products are being produced.

Another assumption may be that the product in question is not complementary. This may be incorrect as we cannot establish whether the product in question depends on one another. For example you cannot supply one product without the other and if the products are complementary then the organisation will have to think about what decision they are going to make.

It has also been assumed that the product which gives the highest contribution should be considered for decision making with regards to the limiting factor. This assumption is too numerical as in reality there may be some problems apportioning the fixed and variable costs which already have been absorbed to the product which its production will use as a result of the decision taken by the management. Therefore if there is no percentage given for apportionment we can not estimate how to apportion the fixed cost and variable cost to the remaining products.

Finally, another assumption may be to assume that the material shortage is the only limiting factor when the management is making a decision. This assumption may have a significant effect on the financial and moral side of the company. For example, if the materials were the only limiting factor and the management decide to discontinue the production of a certain product as it does not give any contribution, this may have an impact on the salary of the employees, as the company will have to pay the staff during idle time, and even if they are relocated to work on another product they won’t be able to fully utilise their best skills and abilities. Another implication may be the moral of the employees, as they may be demoralised when they hear that the company will no longer be producing their product.

4.0 The alternative courses of action

        The alternative courses of action the management team may consider in their decision making may be any of the following options.

        Firstly the organisation may decide to stop the production of a particular item. As illustrated in 1.0 product (024) does not give any contribution and due to this the product was not considered in the rank of production as there is also a shortage in materials. Therefore the management will have to come to a conclusion whether to keep this product or stop the production completely of this item. However, before the management come to any sort of decision they will have to consider the following key factors.

 Firstly, there is the assumption of fixed costs. Generally the fixed costs would still remain the same even if you decided to stop the production of product (024). Nevertheless, if dropping product (024) would result in the elimination of a fixed cost, then to stop the production of product (024) would then be worthwhile; however this is highly unlikely to happen.

Secondly is product (024) complementary to product (060) because if they are then will the dropping of product (024) affect the sales of the new quantity of product (060)?

Finally, what will be the relevant costs for this decision making? Bearing in mind the previous points then the management can come to a decision. If the company decide to stop the production of product (024) then the company will have the alternative decision which may be to buy from outside.

The advantages of discontinuing the production of product (024) and part of product (060) are; that the management will benefit in the difference between the buying cost and the making cost which is the main factor of the decision making. Another advantage may be to abandon the production; it will then enable the organisation to concentrate on the other products which give out the substantial amount of contribution.

The disadvantages of discontinuing the production of product (024) and part of product (060) may be that the financial implications where by the employees still have to be paid either redundancy money or wages if the organisation decides to keep them. Another disadvantage may be that there is a possibility of loosing the customers because if the company decide to discontinue the product the customers the business already have may have to find an alternate supplier, as a result this may cause problems to the organisation. In addition another disadvantage may be that it may be inconvenient for the organisation to make a decision on the staffing which will be idle, therefore the money spent to pay the employees will have to be covered in other areas, and this will then require a highly complicated numerical analysis by the organisation team.

Another alternate course of action the business may take is to buy their goods from outside. In this situation product (024) does not give the company any contribution, in the same way the company can not make the maximum amount of product (060) therefore it will not be a wise decision on economic grounds to buy from outside as both products if or when the relevant costs for making each product are greater than the price quoted by the supplier. However, in this case where product (024) has absorbed a large amount of cost for the production of this item than the selling price as a result the contribution was ‘zero’. So if the company can buy from outside the same product and at a reasonable price and leaves the company with a profit then the management will be satisfied, the same should also apply with product (060) where there is only part of that product produced.

Advantages of buying from outside may be that the business will not have to worry about production of all the products and should enable them to concentrate on producing all the other products other than (024) and (060) which will allow them to produce their goods at the highest quality and keep the customers satisfied. Another advantage may also be that by purchasing goods from abroad will build ties with their companies which may turn out to be beneficial for Mirabeau Ltd in the long run as they can get more business and increase profits.

However, the disadvantages of buying products (024) and (060) from outside may be that the quality of the products from abroad may not be of the highest standard and which may result in the customers not being fully satisfied with their products which may they then result in the company making a loss. Another disadvantage may be that it may be risky relying on the products from outside, as they may be delays or stoppages in delivery from the supplier to Mirabeau Ltd which may then also result in customer’s demand not being met and then also may lead to the company loosing customers and the company may then make a loss.

5.0 Recommendation

After taking into consideration all the information from this report the recommendation I would have for the management team on the decision they will be enforced to make will be; under the assumption that product (024) is not a complementary product to (060) and the relevant cost for decision making, is that buying from outside is cheaper than to produce the product itself, so therefore by buying from outside the company will still have a reasonable amount of contribution and still maintain profits which was one of the key objectives of the organisation and reduce the wastage of stock and still take full advantage of all its employees. So to conclude I would recommend that Mirabeau Ltd should purchase the products (024) and (060) from outside rather then producing them themselves under the assumptions made in this report.