A laboratory has won a 15,000 research grant to be used to purchase equipment that will...

 

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A laboratory has won a 15,000 research grant to be used to purchase equipment that will aid the research of the eight researchers who use the facility. From discussion with the researchers, the laboratory director has identified six critical pieces of equipment that could be purchased. The problem is that the grant will not be sufficient to purchase all the required equipment. The data presented in Table 2 shows the cost per unit of each item. Equipment A Cost 3,018 B 4,009 C 2,200 D 3,868. E 4,129 F 3,877 Table 2: Per unit cost of selected laboratory equipment The laboratory will require two units of equipment C if that equipment is selected. The importance of each piece of equipment is to be judged by the proportion of the researchers who urgently require it for their immediate research. From a survey, only two of the researchers urgently require equipment A and D. Three of the researchers require equipment C. Equipment E and F are urgently required by four and six researchers, respectively. Finally, half of the researchers urgently need equipment B. a. Use branch-and-bound to determine the optimal items to be bought for the lab. [10 marks] b. Will a greedy heuristic result in a different solution for this problem? [5 marks] A laboratory has won a 15,000 research grant to be used to purchase equipment that will aid the research of the eight researchers who use the facility. From discussion with the researchers, the laboratory director has identified six critical pieces of equipment that could be purchased. The problem is that the grant will not be sufficient to purchase all the required equipment. The data presented in Table 2 shows the cost per unit of each item. Equipment A Cost 3,018 B 4,009 C 2,200 D 3,868. E 4,129 F 3,877 Table 2: Per unit cost of selected laboratory equipment The laboratory will require two units of equipment C if that equipment is selected. The importance of each piece of equipment is to be judged by the proportion of the researchers who urgently require it for their immediate research. From a survey, only two of the researchers urgently require equipment A and D. Three of the researchers require equipment C. Equipment E and F are urgently required by four and six researchers, respectively. Finally, half of the researchers urgently need equipment B. a. Use branch-and-bound to determine the optimal items to be bought for the lab. [10 marks] b. Will a greedy heuristic result in a different solution for this problem? [5 marks]

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a Using BranchandBound to Find the Optimal Solution The branchandbound algorithm is an optimization technique used for finding the optimal solution in ... View the full answer