Bantu Ltd. is a large cash and carry warehouses which sells electronics. Bantu Ltd. Purchases the most popular model of calculators (FX 100) directly form the manufacturer at a cost of Sh.250 each. Average sales per a 300 day year are 475 calculators. Whenever an order with the manufacturers is placed, Bantu Ltd, Incurs a cost of Sh.50. The stock holding costs are estimated at Sh.12.50 plus 10% opportunity cost of capital. The lead-time is three days. During the last 50 stock cycles, the demand during the lead-time has generated the following frequency distribution:
Lead time demand
Number of stock cycles
Each time the warehouses runs out of stock, an emergency order is placed with an extra cost of Sh.20 per calculator.
a) The economic order quantity (EOQ) and the reorder level. (16 marks)
b) The total annual relevant costs for the order quantity in (a) above. (4 marks)
(Total: 20 marks)
Ganish Ltd. manufactures a range of five similar products, A, B, C, D and E. the table below shows the quantity of each of the required inputs necessary to produce one unit of each product, together with the weekly inputs available and selling prices of each product.
Weekly inputs available
Raw materials (Kg)
The costs of each input is as follows:
Material Sh.2.10 per Kg
Forming Sh.3.00 per hour
Firing Sh.1.30 per hour
Packing Sh.8.00 per hour
a) Formulate this problem as a Linear Programming problem. (7 marks)
b) The problem has been solved using a computer package and the following final table of a simplex solution has been produced:
Where A, B, C, D and E are the weekly production levels for the five products; X is the amount of raw material that falls short of the maximum available; S, T an U are the respective number of hours short of maximum weekly input of forming, firing and packing time.
i Use this table to find the optimum weekly production plan. (4 marks)
ii Describe the implications of using this plan in terms of unused resources and overall contribution to profit. (3 marks)
iii In the context of this problem explain the meaning of ¡°The dual or shadow price of a resource¡± (3 marks)
iv There is a proposition that the company manufactures an additional product which would sell at Sh.50 per unit. Each unit will need 6 kg of raw material, one hour of forming time, five hours of firing time and one hour of packing time. Is it a worthwhile proposition? (3 marks)
(Total: 20 marks)
(a) Briefly explain four ways in which competitive situations (or games) can be classified. (8 marks)
(b) Kariuki and Nadia are two cousins specializing in hawking business along River road. Kariuki specializes in second hand shirts while Nadia specializes in cheap electronic goods. However, sales have been decreasing partly due to the harsh economic condition in Kenya and partly due to restrictions by the City Council.
Each of the cousins is considering expanding to include in their lines of business, items on which their rivals now have a monopoly. Each knows that the other is considering this expansion and this influences each of their decisions.
Kariuki figures out that if he does not expand his business and his cousin does, it will hurt his trade by Sh.500 of profit per day. If neither of them expands inventory to include the extra product, Kariuki thinks it will boost his net profit by Sh.500 per day due to his superior location. If he expands and his cousin does also, he believes the combination of location and expanded inventory will increase his profits by Sh.1,000 per day. However, if he alone expands and his cousin does not, this will result in no net increase in business.
i Prepare a game matrix and show that a pure strategy does not exist. (4 marks)
ii Solve the above game to determine the average winnings (or losses) each of the cousins would expect. (8 marks)
(Total: 20 marks)
1. Doha Ltd. makes special purpose equipment according to customer specifications. During the past year, one of its loyal customers, Mema Ltd., ordered a specialized equipment to be fabricated for it. Doha Ltd. Finished construction the equipment only to be notified that Mema Ltd. Had recently gone into liquidation and will not therefore take the equipment.
The original price to Mema Ltd. had been agreed at Sh.9,108,000 which included an estimated normal profit mark-up of 10 per cent on total costs. The costs incurred to manufacture the machine were
Direct materials 3,420,000
Direct wages 2,160,000
Fixed; production 1,800,000
Fixed; selling and administration 360,000
After a sustained search, the sales manager of Doha Ltd. Has managed to locate one potential buyer, Ziwa Systems Ltd, which has indicated that it could buy the machine if certain conversion work could be carried out.
Doha Ltd.s production department has made a preliminary assessment which reveals that conversion would entail extra work costed as follows:
Direct materials Sh.576,000
Department X: 3 men for 4 weeks at Sh.27,000 per man/week
Department Y: 1 man for 4 weeks at Sh.21,600 per man/week
20 per cent of direct wages
Fixed production overhead:
Department X: 75 per cent of direct wages.
Department Y: 25 per cent of direct wages.
The following additional information is provided:
1. In the original machine, there were three types of basic materials:
i Type P could now be sold to a scrap merchant for Sh.540,000.
ii Type Q could be sold to a scrap merchant for Shs. 360,000 but it would take 120 hours of labour paid at Shs. 270 per hour to put it into a suitable condition for sale.
iii Type R would need to be scrapped at a cost to Doha Ltd. of Shs.108,000
2. The materials for the conversion are at present in stock. If not needed for the conversion they could be used in the production of another machine in place of materials that would currently cost Sh.684,000.
3. The conversion would be carried out in two departments:
Department X is currently extremely busy and it is estimated that its contribution overheads and profits is Sh.2.50 for every Sh.1 of labour.
Department Y has idle staff, for organizational reasons its labour force cannot be reduced below its present level of four employees, all of whom are paid at the standard rate of Sh.21,600 per week.
4. The designs and specifications of the original machine could be sold in a neighbouring country for a sum of Sh.270,000 if the machine is scrapped.
5. An additional temporary supervisor would have to be engaged for the conversion work at a cost of Sh.162,000. It is the company.s normal practice to charge supervision to fixed overhead.
6. Mema Ltd. Had paid Doha Ltd. A non-returnable deposits of 12% of the selling price.
a) The minimum price that Doha Ltd. should accept from Ziwa Systems Ltd. for the converted machine. Explain clearly how you arrive at your figure. (16 marks)
b) State clearly any assumptions that you have made in arriving at your conclusions in (a)
above. (4 marks)
(Total: 20 marks)
Kaimosi Limited is a multi-division manufacturing company. The manufacture of M101. One of the company.s finished products involves two divisions; Mega and Wazo. Mega division manufactures the chassis for M101 and transfers it to Wazo division where it is reworked, fitted and assembled into the finished product. The two divisions are housed in the same building whose lease is due to expire in two years. time.
Data on the operations of the two divisions for the year just ended is as follows:
Quantity of units (chassis) transferred per year 30,000
Transfer price from Mega to Wazo Sh.30000
Current level of operations 75% of full capacity
Loss for the year Sh.90,000,000
Quantity of units produced and sold 30,000
Price charged outsiders Sh.150,000
Profit made for the year Sh.610,000,000
Mr. Links the general manager of Wazo division, has been considering the possibility of sourcing the chassis from outside suppliers. He has received a quotation from Bush Ltd., a competitor of Mega division offering to supply a minimum of 30,000 and a
maximum of 40,000 units of chassis per year for two years with adequate guarantees as to quality and continuity of suppliers. The unit price would be Sh.22,000. Mr.Links is of the opinion that his division should be allowed to take all its requirement (30,000 units per year) of chassis from Bush Ltd., unless Mega division agrees to cut the unit transfer price to Sh.22,000. He suggests that if Mega division cannot reduce the price it would be better for it to cease operations and the space it now occupies be taken up by Wazo division, which is currently seeking extra warehouse space.
The summarized profit and loss accounts of the divisions for the past year ended 31 October 2001 is as follows:
Production and sales (Physical units)
Fixed overhead (excluding depreciation)
Fixed overhead - depreciation