An Icelandic horse farmer would like to supply her animals with sufficient vitamins A, B, C and D. Two types of feed, Isil and Isi2, are available for this purpose. The prices of both types of feed (in € per 100g), the vitamins they contain (in mg per 100g of feed) and the minimum requirement of vitamins per Icelandic horse (in mg per day) are given in the following table. л в 6 7 1 4 C D Costs Isil 6. 3. 1.50 Isi2 10 9. 1.00 minimum requirement per horse 22 71 120 72 How must the breeder compose her feed from the two different feed types in order to keep the financial expenditure for this as low as possible and at the same time cover the vitamin requirements of the Icelandic horses? It should be noted that an Icelandic horse may not receive more than 2 kg feed per day. (a) Set up the optimisation problem (objective function/target, constraints, non-negativity con- straints). (b) Draw the feasible set and determine the vertices. (c) Determine graphically the optimal feed mixture and provide the optimal costs for the feed per Icelandic horse. Describe what you are doing.
An Icelandic horse farmer would like to supply her animals with sufficient vitamins A, B, C and D. Two types of feed, Isil and Isi2, are available for this purpose. The prices of both types of feed (in € per 100g), the vitamins they contain (in mg per 100g of feed) and the minimum requirement of vitamins per Icelandic horse (in mg per day) are given in the following table. л в 6 7 1 4 C D Costs Isil 6. 3. 1.50 Isi2 10 9. 1.00 minimum requirement per horse 22 71 120 72 How must the breeder compose her feed from the two different feed types in order to keep the financial expenditure for this as low as possible and at the same time cover the vitamin requirements of the Icelandic horses? It should be noted that an Icelandic horse may not receive more than 2 kg feed per day. (a) Set up the optimisation problem (objective function/target, constraints, non-negativity con- straints). (b) Draw the feasible set and determine the vertices. (c) Determine graphically the optimal feed mixture and provide the optimal costs for the feed per Icelandic horse. Describe what you are doing.
Chapter6: Systems Of Equations And Inequalities
Section6.5: Systems Of Inequalities
Problem 9ECP
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Transcribed Image Text:An Icelandic horse farmer would like to supply her animals with sufficient vitamins A, B, C and D.
Two types of feed, Isil and Isi2, are available for this purpose. The prices of both types of feed (in
€ per 100g), the vitamins they contain (in mg per 100g of feed) and the minimum requirement of
vitamins per Icelandic horse (in mg per day) are given in the following table.
A
в с D
costs
Isil
6.
6
3
1.50
Isi2
9 1.00
1
4
10
minimum requirement per horse 22 71 120 72
How must the breeder compose her feed from the two different feed types in order to keep the financial
expenditure for this as low as possible and at the same time cover the vitamin requirements of the
Icelandic horses? It should be noted that an Icelandic horse may not receive more than 2 kg feed per
day.
(a) Set up the optimisation problem (objective function/target, constraints, non-negativity con-
straints).
(b) Draw the feasible set and determine the vertices.
(c) Determine graphically the optimal feed mixture and provide the optimal costs for the feed per
Icelandic horse. Describe what you are doing.
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