Question 1 Linear Programming (15 marks)

The junior marketing manager would like you to assist in providing information for a marketing strategy she is proposing at the annual general meeting next month. She is focusing only on a new innovative solver-based paint that can be washed off using water instead of mineral turpentine. The marketing manager wants to know the optimal product mix that should be offered. Below is an estimation of the costs of the five sizes that the paint can be purchased, only two of the five sizes can be manufactured due to constraints of the packaging machine which are unrelated to constraints in the below table.

	Paint Tin Sizes
	500ml	1 litre	4 litres	10 litres	15 litres
Selling Price	$17.00	$25.00	$90.00	$180.00	$270.00
Costs per tin:
Raw materials	$2.00	$5.00	$54.00	$130.00	$200.00
Direct labour	$4.00	$6.00	$14.00	$16.00	$20.00
Variable overhead	$2.00	$2.00	$8.00	$20.00	$36.00
Fixed overhead	$3.00	$6.00	$8.00	$10.00	$15.00

Each of the five products goes through the same manufacturing process which consists of weighing raw materials, dispersion, pre-mixing, pigment grinding and stability inspection. The time for each batch is in the table below.

	Collecting and weighing RM	Mixing		Colour pigment added			Packaging
	Hours required per batch
500ml	1		1		0.25	4
1 litre	2		2		0.5	3
4 litres	2		3		0.5	2
10 litres	3		4		1	1
15 litres	3		5		1	1
Hours Availalbe	1,200		600		400	1,200

Required:

1. Formulate a linear program to determine the expected mix of paint tins, ensuring that the maximum profit is obtained. Discuss the key features of your results taking into consideration the practical limitations of using Solver. (8 marks)
2. Discuss two possible ways all 5 sizes could be manufactured. Provide financial information to support your recommendations and clearly illustrate how your proposals impact the production mix and the firm's contribution margin. (7 marks)