2. A food factory makes three types of cereals, A, B and C, from a mix of several ingredients: Oates, Apricots, Coconuts and Hazelnuts. The cereals are packaged in 1 kg boxes. The following table provides details of the sales price per box of cereals and the production cost per ton (1000 kg) of cereals respectively. Cereal A Cereal B Cereal C The following table provides the purchase price per ton of ingredients and the maximum availability of the ingredients in tons respectively. Sales price per box ($) Production cost per ton 2.50 4.00 2.00 2.80 3.50 3.00. Ingredients Purchase price ($) per ton Maximum availability in tons Oates 100 120 80 200 Apricots Coconuts Hazelnuts Cereal A Cereal B Cereal C 9522 10 The minimum daily demand (in boxes) for each cereal and the proportion of the Oates, Apricots, Coconut and Hazelnuts in each cereal is detailed in the following table, Proportion of Minimum demand (boxes) Oates Apricots Coconuts 1000 0.8 0.1 0.05 700 0.65 0.2 0.05 750 0.5 0.1 0.1 Hazelnuts 0.05 0.1 0.3 a) Let xij≥0 be a decision variable that denotes the number of kg of ingredient i, where i could be Oates, Apricots, Coconuts, Hazelnuts, used to produce Cereal j, here j is one of A,B,C, (in boxes). Formulate an LP model to determine the optimal production mix of cereals and the associated amounts of ingredients that maximises the profit, while satisfying the constraints.
2. A food factory makes three types of cereals, A, B and C, from a mix of several ingredients: Oates, Apricots, Coconuts and Hazelnuts. The cereals are packaged in 1 kg boxes. The following table provides details of the sales price per box of cereals and the production cost per ton (1000 kg) of cereals respectively. Cereal A Cereal B Cereal C The following table provides the purchase price per ton of ingredients and the maximum availability of the ingredients in tons respectively. Sales price per box ($) Production cost per ton 2.50 4.00 2.00 2.80 3.50 3.00. Ingredients Purchase price ($) per ton Maximum availability in tons Oates 100 120 80 200 Apricots Coconuts Hazelnuts Cereal A Cereal B Cereal C 9522 10 The minimum daily demand (in boxes) for each cereal and the proportion of the Oates, Apricots, Coconut and Hazelnuts in each cereal is detailed in the following table, Proportion of Minimum demand (boxes) Oates Apricots Coconuts 1000 0.8 0.1 0.05 700 0.65 0.2 0.05 750 0.5 0.1 0.1 Hazelnuts 0.05 0.1 0.3 a) Let xij≥0 be a decision variable that denotes the number of kg of ingredient i, where i could be Oates, Apricots, Coconuts, Hazelnuts, used to produce Cereal j, here j is one of A,B,C, (in boxes). Formulate an LP model to determine the optimal production mix of cereals and the associated amounts of ingredients that maximises the profit, while satisfying the constraints.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:2. A food factory makes three types of cereals, A, B and C, from a mix of several ingredients:
Oates, Apricots, Coconuts and Hazelnuts. The cereals are packaged in 1 kg boxes. The
following table provides details of the sales price per box of cereals and the production
cost per ton (1000 kg) of cereals respectively.
Cereal A
Cereal B
Cereal C
The following table provides the purchase price per ton of ingredients and the maximum
availability of the ingredients in tons respectively.
Sales price per box($) | Production cost per ton
2.50
4.00
2.00
2.80
3.50
3.00.
Ingredients Purchase price ($) per ton Maximum availability in tons
Oates
100
120
80
200
Apricots
Coconuts
Hazelnuts
Cereal A
Cereal B
Cereal C
8522
The minimum daily demand (in boxes) for each cereal and the proportion of the Oates,
Apricots, Coconut and Hazelnuts in each cereal is detailed in the following table,
Minimum demand (boxes) Oates
1000
0.8
700
0.65
750
0.5
10
Proportion of
Apricots Coconuts Hazelnuts
0.1
0.05
0.05
0.2
0.05
0.1
0.1
0.1
0.3
a) Let Xij
≥ 0 be a decision variable that denotes the number of kg of ingredient i, where
i could be Oates, Apricots, Coconuts, Hazelnuts, used to produce Cereal j, here j is
one of A,B,C, (in boxes). Formulate an LP model to determine the optimal production
mix of cereals and the associated amounts of ingredients that maximises the profit, while
satisfying the constraints.
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