Tiyende Pamodzi Limited (TP Ltd), a furniture manufacturer based in Kitwe, has two automated machines, X and Y, through which timber passes in order to produce decorative lampstand centres. There are production capacity constraints and TP Ltd has decided to produce only one of the two lampstand models, T or M, in the year 31^st March 2021. The following forecast information is available for the year to 31^st March 2021.

Model T Model M

Maximum sales potential 7,400 10,000

Selling price K45 K40

Machine X hours 0.25 0.150

Machine Y hours 0.20 0.225

Machines X and Y have maximum operating hours of 1,700 and 1,920 hours respectively. Lampstand production is the sole use available for production capacity. The maximum quantity of timber available is 17,000 metres. Each lampstand requires a two metre length of timber which may be purchased in lengths as required at K2.50 per metre.

Variable machine overhead for machines X and Y is estimated at K25 and K30 per machine hour respectively. All units are sold in the year in which they are produced.

1. Calculate the contribution per unit for each lampstand model (10 Marks)
2. Decide which of the lampstand models, T or M, should be produced and sold in the year to 31^st March 2021 in order to maximise profit. You should clearly state the number of units to be produced and sold (30 Marks)
3. Calculate the amount of contribution that will be generated by the number of units produced in b) above. (10 Marks)