Question 2 - Linear Programming

Pandora Chocolates manufactures 3 main products: Jelly Choco, Spotted Chocolate and Nuke Delight and has started to supply to independent supermarkets and general stores. Although the company does make other chocolate treats these are seasonal and change yearly. The raw material ingredients that the three products use are all the same, it's the process of mixing and cooking that determine how the product will turn out.

Jelly Choco are small chocolates which come in 5 flavours and every 110g pack contains 5 of each flavour. Pandora Chocolates packages 20 individual packets into boxes. To produce these chocolates 1.5kg of raw material is required, 2 hours of labour and overhead is applied at a rate of 150% of direct labour.

Spotted Chocolate is a similar-sized chocolate to Jelly Choco and comes in different colours. These are packaged in small cardboard boxes and weigh 130g per box. To produce this chocolate requires 2 kg of raw material, 2.5 hours of direct labour and overhead is applied at 150% of direct labour.

Nuke Delight is sugar-coated chocolate which is soft and chewy to eat and is Pandora Chocolates' biggest seller. Pandora Chocolates has kept to traditional flavours and will once a year bring in a limited edition flavour for a set period. Nuke Delight requires 3 kg of raw material, and 3 hours of direct labour with overhead applied at 150%. A box contains 10 Nuke Delight packages.

Each of these 3 products goes through the same manufacturing process which consists of mixing, cooking and packaging. Jelly Choco are sold for $1.60 per pack, Spotted Chocolate for $1.70 and Nuke Delight at $2.00 per pack.

	SP	RM	DL	OH
Jelly Choco	$ 1.60	$ 0.30	$ 0.20	$ 0.30
Spotted Chocolate	$ 1.70	$ 0.50	$ 0.10	$ 0.15
Nuke Delight	$ 2.00	$ 0.40	$ 0.27	$ 0.41

	Mixing	Cooking	Packaging
	HOURS REQUIRED
Jelly Choco	4	8	3
Spotted Chocolate	10	3	2
Nuke Delight	8	8	2
HOURS AVAILABLE	800	1200	1000

Required:

1. Formulate a linear program to determine the expected mix of chocolates to ensure the maximum profit will be created. Show all supporting calculations and solve using a computer package (eg solver in Excel) to derive the optimum solution. (5 marks)
2. Upon reviewing the constraints, it has been noticed that the majority of direct labour has been incorrectly allocated to the Nuke Delights and should only be $0.17 per box. Formulate a second linear program taking into consideration the changes. (5 marks)
3. Discuss the results from both of the Solver solutions. What financial and non-financial issues should be considered when making a decision on the optimal mix? (5 marks)