Advanced : Linear programm ing and trans fer pri cing plus the practical prob lems of implementing a market price based system . . .

Megacorp pic is a large multi-divisional company operating pnma~1ly within the UK. One of its divisions, Aira, operates a small production plant solely devoted to the manufacture of three materials, Ingots, Jars and Knuts. All the output of the plant is transferred to a factory operated by the Blackside division of Megacorp pic where the three products are used as the major raw materials in the production of two products, Lemons and Mavericks. These products are then sold externally.

In the Aira division's production plant. three main production operations are carried out, namely Forging, Gnnding and Hea~n~.

These take place using different types of equipment, each of hm1ted capacity. To produce one unit of each of the three products requires different amounts of time in the three processes, as follows

Conversion of Ingots, Jars and Knuts into lemons and Mavericks also requires three processes, Rolling, Stirring and Turning. To make a lemon requires one Ingot, two Jars and two Knuts; a Maverick requires three Ingots, two Jars and one Knut. The processing times and availabilities are as follows:

The raw materials used in the production of Ingots, Jars and Knuts are otherwise worthless by-products from other production processes in Megacorp pic, but each production process in both the Aira and the Blackside divisions has a variable cost of £1 per hour to operate. The current market price of Lemons is £47 each, and Mavericks £56 each.
Requirements

(a) Fonnulate the overall production problem of the two divisions as a linear program designed to maximise the total contribution to profit of the two divisions combined.
(6 marks)

(b) The LP solution indicates that only Grinding and Heating are limiting resources. Grinding has a shadow (i.e. dual) price per hour of 62.5p and Heating 31.25p. The optimum daily production is 30 lemons and 27.5 Mavericks. Using these shadow prices:
(i) Calculate transfer prices for Ingots, Jars and Knuts.
(3 marks)
(ii) Calculate the total contribution the production plan generates for each division. . (2 ma.rks)

(c) Describe how divisional profits would be affected 1f the Alra division provided extra capacity so that limiting resources now existed only in the Blackside division. {4 marks)

(d) Discuss the practical problems and possible advantages of Megacorp pic implementing a market price based system of transfer pricmg rather than a system based on shadow prices.

Transcribed Image Text:

To make one unit of Ingots Jars Time required in hours for each production process Grinding Forging 5 1 Heating 12 2 2 2