Question 4
(10 marks)
On weekends, Tatekulu Ngwala spends his spare time carving toy figures from wood. The two
types of toys that he carves are the Incredible Hulk and Iron Man. Each Incredible Hulk needs
15 minutes of machine time and 12 minutes finishing time, while every Iron Man requires 20
minutes of machine time and 1Ominutes finishing time. Only Japie operates the machine, and
he has only 15 hours available. A worker with an available time of 10 hours does the finishing.
Japie received an order for 15 Iron Man toys (which still need to be produced) for next week.
Usually Japie sells all the toys he produces. Incredible Hulk toys make a profit of N$6 per toy,
and Iron Man gives a profit of N$5 per toy.
The total fixed cost for the Hulk toy is N$2 while for Iron Man it is N$4. Tatekulu Ngwala was
informed that you are able to assist him with a production-related problem .
REQUIRED:
Marks
Use the graphical method to determine the optimum combination of toy men (Hulk (10)
& Iron) to be made and sold in order to maximise profits, by algebraically
calculating the profit at each intersection within the feasible region.
Round down to the lower unit. E.g. 3.6 becomes 3.
Show all your workings!
Total
10
Question 5
(20 Marks)
Henry Company (HC) provides skilled labour to the building trade. A builder has recently
asked them to bid for a kitchen fitting contract for a new development of 600 identical
apartments. HC has not worked for this builder before.
The general kitchen fitting process begins with site preparation, which includes inspection,
measurement verification, and confirmation that all necessary materials and tools are
available. The team, comprising carpenters, plumbers, electricians, and assistants, marks the
layout for cabinets, plumbing, and electrical points before installation begins. Wall and base
cabinets are fitted first, followed by plumbing connections for the sink and water outlets, and
electrical installations for lighting and appliances.
Once the structural components are in place, countertops and splashbacks are installed, and
final finishes such as handles, hinges, and trims are added. The process concludes with a
thorough quality inspection, testing of plumbing and electrical systems, and cleaning of the
work area to ensure the kitchen is fully functional, aligned, and ready for use.
Cost information for the new contract is as follows:
Labour for the contract is available. HC expects that the first kitchen will take 24 man-hours
to fit, but thereafter the time taken will be subject to a 95% learning rate . After 200 kitchens
are fitted, the learning rate will stop, and the time taken for the 200th kitchen will be the time
taken for all the remaining kitchens. Labour cost is N$15 per hour.
Overheads are absorbed on a labour hour basis. HC has collected overhead information for
the last four months and this is shown below:
5