A distillery in Scotland uses i = 1,...,m unblended whiskies (inputs) to create blended whiskies (products)...

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A distillery in Scotland uses i = 1,...,m unblended whiskies (inputs) to create blended whiskies (products) j = 1,...,n with properties k = 1,..., p. Unblended whisky i measures ai,k on scale k. Assume that the properties of the blended whiskies are a weighted average by volume of the properties in the input unblended whiskies. Define an appropriate set of variables, and use this set to model the following: (a) Property k = 11 should fall between 45 and 48 on all products. (b) Product j = 14 must have all properties k = 5,..., 9 between 90 and 95. (c) Product j = 26 must measure at least 116 on property k = 15. (d) No product should measure more than 87 on property k = 8. (e) Products 6 through 11 should combine input whisky 1 with other input whiskies in a most the ratio 3:7. (f) Input whiskies 4 and 7 should be in the ratio 2:3 for all blended whiskies. (g) At least one-third of the total output of blended whiskies must come from inputs i = 3,4,5,6. (h) No more than 5% of the total output can come from input i = 13. A distillery in Scotland uses i = 1,...,m unblended whiskies (inputs) to create blended whiskies (products) j = 1,...,n with properties k = 1,..., p. Unblended whisky i measures ai,k on scale k. Assume that the properties of the blended whiskies are a weighted average by volume of the properties in the input unblended whiskies. Define an appropriate set of variables, and use this set to model the following: (a) Property k = 11 should fall between 45 and 48 on all products. (b) Product j = 14 must have all properties k = 5,..., 9 between 90 and 95. (c) Product j = 26 must measure at least 116 on property k = 15. (d) No product should measure more than 87 on property k = 8. (e) Products 6 through 11 should combine input whisky 1 with other input whiskies in a most the ratio 3:7. (f) Input whiskies 4 and 7 should be in the ratio 2:3 for all blended whiskies. (g) At least one-third of the total output of blended whiskies must come from inputs i = 3,4,5,6. (h) No more than 5% of the total output can come from input i = 13.

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Set of unblended whiskies I 1 2 m Set of blended whiskies J 1 2 n Set of properties K 1 2 p Paramete... View the full answer