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A hot-air baloon containing 3 men was caught in a hurricane and deposited on a deserted island. There are two sources of food on the island: fish and coconuts. After some experimentation, the men have found that, on average, one man can catch 4 ounces of fish each hour or he can gather 10 ounces of coconut meat in an hour. They know that one ounce of fish provides 14 g of protein, 80 calories, and 100mg of vitamin A. An ounce of coconut meat provides 2 g of protein, 200 calories, and 50mg of vitamin A. The minimum daily requirements for each man are: 42 g of protein, 2,000 calories, and 600 mg of vitamin A. The men wish to minimize the amount of time needed to gather food so they can work on finding a way to get off the island.
Let f = the number of hours spent catching and preparing fish and c = the number of hours gathering coconuts and preparing coconut meat. The castaway's object is to minimize 1/4 f + 1/10 c.
1. Write a set of constraints to fit the problem as described above.
2. How much time should the castaways spend on each activity to minimize their objective function. Show all of your work to justify your solution.
3.After one month, the castaways have gathered all of the coconuts close to their camp. They now must walk far enough away from their camp to gather coconuts that their optimal behavior is to only catch fish to minimize their objective. What is the maximum number of ounces of coconut meat they can now gather in one hour?
And for extra credit. Graph the castaways constraints to show the region of feasible solutions to the linear programming problem.
Good luck.
Let f = the number of hours spent catching and preparing fish and c = the number of hours gathering coconuts and preparing coconut meat. The castaway's object is to minimize 1/4 f + 1/10 c.
1. Write a set of constraints to fit the problem as described above.
2. How much time should the castaways spend on each activity to minimize their objective function. Show all of your work to justify your solution.
3.After one month, the castaways have gathered all of the coconuts close to their camp. They now must walk far enough away from their camp to gather coconuts that their optimal behavior is to only catch fish to minimize their objective. What is the maximum number of ounces of coconut meat they can now gather in one hour?
And for extra credit. Graph the castaways constraints to show the region of feasible solutions to the linear programming problem.
Good luck.
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