Answer Happy

A1 ACME International manufactures machine tools from four production centres in Liverpool, UK; Toulon, France; and Hamburg, Germany. These production facilities supply four distribution centres, located in Lyon, France; London, UK; Frankfurt, Germany; and Barcelona, Spain. Table 1.1 below gives the production capacity at each of these facilities and the quantities demanded by the distribution centres. In this situation, the total quantity demanded is balanced with the total quantity produced. The shipping costs for this distribution network, in pounds, are shown in Table 1.2 below. Table .11: Production and demand data Factory Production capacity Distribution Daily Demand (units/day) 150 (units/day) Centre Lyon 180 275 London 150 325 Liverpool Toulon Hamburg Frankfurt Barcelona Table 1.2: Shipping costs From/to Lyon London Frankfurt Barcelona Liverpool 5 7 17 Toulon 12 4 Hamburg 8 11 8 15 9 185 235 a. Check that the daily distribution requirements can be met and draw a graphical representation of the ACME International distribution problem. (2 MARKS) b. Define the input data required for the construction of a model for decision making. (2 MARKS) c. Construct an LP to minimise the cost of meeting distribution centre demand. Explain all steps in the formulation of the problem. Please note that you don't have to solve the LP (8 MARKS)