4. A new Uranium mine, in Namibia has decided, as a matter of urgency, to build a new road as an upgrade to the existing one to facilitate efficient transportation of materials. The road works has been divided into five stages which are built simultaneously. Within Namibia, there are six large companies to undertake the construction of any of the five stage and each company has been invited to submit a tender for each stage of the project. The tenders (in millions of Namibian dollars) are as follows: Company A BCDEF Stage 1 49 53 54 46 57 50 2 84 92 86 86 94 82 3 63 62 67 62 66 65 4 82 No bid 78 76 83 80 5 68 67 68 No bid 70 72 OL 19 D a. Assuming that none of the companies is large enough to undertake the work of more than one stage, advise the mine how the five contracts should be allocated. What is the minimum total cost for the project? (10) Midas mining company is about to replace some of their existing equipment with two new types of computer controlled machinery. The first type, called a Lathe, performs precision marble cutting operations automatically whereas the other machine, called Mander, is used for high- speed moving of parts on to and off a Lathe. The company has decided that upto $1,2 million can be spent on this new equipment, given that a Lathe will cost $20,000 and a Mander, $10,000. Lathes can be installed individually and each one will replace existing equipment which has a market value of $4,000. On the other hand, a Mander is only worth installing if it can be linked to two Lathes and this arrangement (2 Lathes and a Mander), will replace equipment which has a market value of $10,000. You can assume that all the existing equipment can be sold off and the revenue generated can be used to increase the budget for the new equipment. The number of both skilled and unskilled labour demanded to operate the new equipment is less compared to the current equipment. Each Lathe installed individually will make redundant one skilled worker whereas each combination of two Lathes and a Mander will result in two skilled workers and two unskilled workers becoming redundant. Midas have agreed with workers that each redundant skilled worker will be paid $9,000 and $6,000 for each unskilled worker. Note that there is a separate budget for worker payouts but should not exceed $0.9 million. 1. Assuming that each skilled worker employed costs the company $12,000 a year and each unskilled worker employed costs $8,000 a year, formulate a model to determine the number of Lathes and Manders which should be installed to maximise the annual savings that will result from the reduced number of workers that will be required. (4) Determine the optimum number of Lathes and Manders to be installed. What is the annual savings in Labour costs that will produce and how many redundancies will be involved? (8) 11.