HIJ Pte Ltd (HIJ) produces silverware.

It produces 3 lines of silver cutlery: the Harmon, the Ikea, and the Jenny.

There are 3 consecutive stages to producing the cutlery shaping, smoothing and decorating. Each involves the use of specialised machinery.

HIJ operates a just-in-time manufacturing policy: no inventory of closing stocks or work in progress is held.

The time taken in minutes to machine each set of cutlery is as follows:

	Harmon	Ikea	Jenny
Shaping	3	3	2
Smoothing	5	4	3
Decorating	2	2	2

The shaping machines cost $1,000 an hour to operate, the smoothing machines cost $2,000 an hour and the decorating machines cost $4,000 an hour. Machining costs are 100% variable. There are plenty of machines available and their availability do not limit production in any way.

The following relates to other items of cost per set of cutlery:

	Harmon	Ikea	Jenny
Silver (grammes)	300	350	500
Labour 1 worker (minutes)	7	9	12

Silver costs $700 per kilogramme, and labour is paid $40 per hour. There are 4 skilled craftsmen who each work a 40-hour week for each 4-week month. Overtime is not possible due to trade union constraints, and hiring additional craftsmen with suitable experience is not possible in the short to medium term.

Factory overheads amounted to $4,000,000 per annum. Fixed costs are absorbed per labour hour.

The Harmon sells for $1,000 a set, the Ikea sells for $1,200 a set and the Jenny sells for $800 a set. Monthly demand is for 2,500 Harmon, 3,000 Ikea and 1,000 Jenny.

An external supplier has approached HIJ offering to make cutlery on HIJs behalf for $700 per Harmon, $650 per Ikea and $750 per Jenny.

Required:

a) Use the concepts of relevant costing to calculate the incremental cost to make each product, and the corresponding contribution margin (in $).

b) Calculate a production plan to maximise HIJs contribution margin (in $). Include in your production plan how many of each product HIJ should purchase from the external supplier. (15 marks) [Hint: identify the work constraint and use the constraint to work out a production plan]