Patches is a cat who eats cat food for breakfast. Patches requires a breakfast diet that includes at least 40g of protein, at least 90g of iron but no more than 144g of carbs a week. His two favourite brands are Kitty Kibble and Cat Snack. Kitty Kibble contains Ig of protein, 11g of iron and 6g of carbohydrates per box. Cat Snack contain 5g of protein, 5g of iron and 6g of carbs per box. Kitty Kibble costs $4 a box, Cat Snack costs $2 a box. Patches' owner wants to minimise how much money they spend on cereal while meeting Patches' dietary requirements. 1. Construct a table showing: the number of the elements required for each item ● the amount of each element available or the minimum requirements of each element. 2. State the objective function and determine the constraints for each element. ● 3. Item Kitty Kibble Cat Snack Minimum Maximum Protein (g) Objective Function: Let x represent the brand of Kitty Kibble. Let y represent the brand of Cat Snack. ● Ries 4. Produce a labelled graph showing the feasible region. (10) x 1 5 40 (KAL (57) Iron (g) 11 5 90 144 00 Therefore, the objective function will be: Minimise - 4x + 2y Carbohydrates (g) 6 6 **dy24 " 144 5. Find the optimal solution by considering the feasible points. 6. Determine the wastage or oversupply of elements for the optimal solution. 7. Now investigate changes to the original scenario such as: Cost ($/box) 4 2 - the impact on the optimal value when the objective function is changed the impact on the optimal value, and wastage and oversupply, when changes are made to the original constraints by: o changing the available amounts of minimal requirements o changing the number of elements or items required o adding a further constraint (such as a time lipit). T

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter6: Ratio, Proportion, And Probability

Section6.1: Ratios And Rates

Problem 40E

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Transcribed Image Text:tigate Patches is a cat who eats cat food for breakfast. Patches requires a breakfast diet that includes at least 40g of protein, at least 90g of iron but no more than 144g of carbs a week. His two favourite brands are Kitty Kibble and Cat Snack. Kitty Kibble contains Ig of protein, 11g of iron and 6g of carbohydrates per box. Cat Snack contain 5g of protein, 5g of iron and 6g of carbs per box. Kitty Kibble costs $4 a box, Cat Snack costs $2 a box. Patches' owner wants to minimise how much money they spend on cereal while meeting Patches' dietary requirements. 1. Construct a table showing: ● the number of the elements required for each item ● the amount of each element available or the minimum requirements of each element. 2. State the objective function and determine the constraints for each element. 3. Item Kitty Kibble Cat Snack Objective Function: Let x represent the brand of Kitty Kibble. Let y represent the brand of Cat Snack. Minimum Maximum ● Protein (g) 1 5 40 ● 1 Page 1 of 4 4. Produce a labelled graph showing the feasible region. (0.04) (150) (0,4) (57) Iron (g) 11 5 90 x+6y144 - (20 €) Therefore, the objective function will be: Minimise = 4x + 2y Carbohydrates (g) 6 6 **Sy 5. Find the optimal solution by considering the feasible points. 6. Determine the wastage or oversupply of elements for the optimal solution. 7. Now investigate changes to the original scenario such as: 7 (46,00) 144 O adding a further constraint (such as a time lipit). lispit). the impact on the optimal value when the objective function is changed Cost ($/box) 4 2 - the impact on the optimal value, and wastage and oversupply, when changes are made to the original constraints by: o changing the available amounts of minimal requirements o changing the number of elements or items required

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