You are trying to decide how many vitamin pills to take. SuperV brand vitamin pills each contain 2 milligrams of vitamin X, 1 milligram of vitamin Y, and 1 milligram of vitamin Z. Topper brand vitamin pills each contain 1 milligram of vitamin X, 1 milligram of vitamin Y, and 2 milligrams of vitamin Z. You want to take enough pills daily to get at least 12 milligrams of vitamin X, 10 milligrams of vitamin Y, and 12 milligrams of vitamin Z. However, SuperV pills cost 4 cents each and Toppers cost 3 cents each, and you would like to minimize the total cost of your daily dosage. (a) Formulate a linear optimization model that can used to solve this problem. (b) How many of each brand of pill should you take? (c) Formulate the dual of the standard linear optimization model in part (a). (d) How would changing your daily vitamin requirements affect your minimum cost? or What are the dual prices for each cons
You are trying to decide how many vitamin pills to take. SuperV brand vitamin pills
each contain 2 milligrams of vitamin X, 1 milligram of vitamin Y, and 1 milligram
of vitamin Z. Topper brand vitamin pills each contain 1 milligram of vitamin X, 1
milligram of vitamin Y, and 2 milligrams of vitamin Z. You want to take enough pills
daily to get at least 12 milligrams of vitamin X, 10 milligrams of vitamin Y, and 12
milligrams of vitamin Z. However, SuperV pills cost 4 cents each and Toppers cost 3
cents each, and you would like to minimize the total cost of your daily dosage.
(a) Formulate a linear optimization model that can used to solve this problem.
(b) How many of each brand of pill should you take?
(c) Formulate the dual of the standard linear optimization model in part (a).
(d) How would changing your daily vitamin requirements affect your minimum
cost? or What are the dual prices for each cons
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