Question 2 Linear Programming (10 marks)

WB has been inundated with customers wanting to book their cars for conversion. To assist with scheduling and planning the following costs and hours have been recorded.

	Car battery modifications
	Hatch	Sedan	Wagon	SUV	4WD
Selling Price	$7,000.00	$7,500.00	$9,500.00	$8,400.00	$12,500.00
Costs:
Raw materials	$1,200.00	$1,700.00	$3,000.00	$2,400.00	$3,500.00
Direct labour	$2,800.00	$2,250.00	$3,500.00	$2,800.00	$4,500.00
Variable overhead	$1,120.00	$900.00	$1,400.00	$1,120.00	$1,800.00
Fixed overhead	$560.00	$450.00	$700.00	$560.00	$900.00

Each of the five makes of cars goes through the same manufacturing process which consists of measuring and assessing, engineering, mechanical works and testing. The time in hours for each make is shown below in the table.

	Measuring and assessing	Engineering	Mechanical works	Testing
	Hours required per car
Hatch	1	1	1.5	0.5
Sedan	1	2	1.75	1.5
Wagon	1	1	1	0.5
SUV	2	3	0.5	0.5
4WD	2	2	1	1
HOURS AVAILABLE PER MONTH	720	800	640	320

Required:

1. Formulate a linear program to determine the expected mix of cars to convert, ensuring that the maximum profit is obtained (2 marks).
2. Discuss the key features of your results taking into consideration the limitations of using Solver for planning purposes. (2 marks)
3. Taking into consideration all the information provided, what strategies do you recommend WB take to improve cost and the level of output? (4 marks)
4. An assumption of LP is that there is linearity. How does that apply in practice? Discuss this assumption making reference to the solution for WB (2 marks)