Question: A car manufacturer is looking to reorganize and increase the efficiency of its manufacturing operations, and is currently looking at an engine assembly line, which makes three different engines (1.8, 2.0 and 2.5litre). The prices charged for the engines are £2,500, £2,850 and £3,750 respectively, while the inputs required to make each of the engines are listed in the table below:
|
Product
|
Basic
|
Medium
|
High
|
Max. Available
|
|
Aluminium
|
10 units
|
11 units
|
12 units
|
52,000
|
|
Other Metals
|
5 units
|
7 units
|
6 units
|
30,000
|
|
Other Materials
|
6 units
|
4 units
|
9 units
|
28,000
|
|
Labour
|
2 hours
|
2 ¼ hours
|
2 ½ hours
|
10,000
|
The costs for the inputs are £25 per hour for Labour and £100, £120 and £35 per unit for Aluminium, Other Metals and Other Materials, respectively. There is also a maximum daily demand for the engines, which is 4,000 1.8litre, 3,500 2.0litre and 2,000 2.5litre.
Formulate this problem as a linear program and use Excel's Solver to arrive at a solution. Write a short report describing your procedure, justify your formulation and give a recommendation to the firm on the best daily production mix.