A business in the food industry is currently holding 2,000 tonnes of material in bulk storage. This material deteriorates with time, and so in the near future it needs to be repackaged for sale or sold in its present form.

The material was acquired in two batches: 800 tonnes at a price of £40 a tonne and 1,200 tonnes at a price of £44 a tonne. The current market price of any additional purchases is £48 a tonne. If the business were to dispose of the material, it could sell any quantity but only for £36 a tonne; it does not have the contacts or reputation to command a higher price.

Repackaging this bulk material may be undertaken to develop either Product A or Product X.

No weight loss occurs with repackaging, that is, one tonne of material will make one tonne of A or X. For Product A, there is an additional cost of £60 a tonne, after which it will sell for £105 a tonne. The marketing department estimates that 500 tonnes could be sold in this way.

In the development of Product X, the business incurs additional costs of £80 a tonne for repackaging. A market price for X is not known and no minimum price has been agreed. The management is currently engaged in discussions over the minimum price that may be charged for Product X in the current circumstances. Management wants to know the relevant cost per tonne for Product X so as to provide a basis for negotiating a profitable selling price for the product.

Required:

Identify the relevant cost per tonne for Product X, given sales volumes of X of:

(a) up to 1,500 tonnes

(b) over 1,500 tonnes, up to 2,000 tonnes

(c) over 2,000 tonnes.

Explain your answer.