Question 1 (25 marks) Namibia Enterprises produces a single product called product N. The company requires 30 units in October, 30 units in November and 20 units in December. The demand is supposed to be met every month. However, should there be a demand backlog, the cost of such a backlog per unit is N$5 per each month. This means that if 1 unit demanded in October is only satisfied in December, the backlog cost will be N$5 x 2 months = N$10. All the demand should be met by Page 14 of 15 the end of December. The following table contains the monthly production capacity and production cost per unit:

Month	Production capacity	Production cost per unit
October	35 units	N$400
November	30 units	N$420
December	35 units	N$410

Each unit in inventory incurs a holding cost of N$20 at the end of each month.

Requirement	Marks
1.1	Namibia Enterprises aims to reduce the cost of production, cost of backlog and inventory holding costs. Construct a balanced transportation problem that can be used to solve this problem.	5
1.2	Using the Vogel's approximation method (VAM), find the basic feasible solution of the problem formulated in (1.1) above.	10
1.3	Using the Modified Distribution Method (MODI), find the optimum solution to the problem in (1.2) above	10
Total	2