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1. Ruby Flyer is a UD student who makes cupcakes in her spare time. She is famous for making 2 types of cupcakes: Nilla Sprinkles (vanilla) and Midnight Magic (chocolate). Both types require eggs in their recipes and Ruby just purchased 240 organic eggs from a local farm. According to the recipes, 3 eggs are required to make 1 dozen of Nilla Sprinkles cupcakes and 2 eggs are required to make 1 dozen of Midnight Magic cupcakes. Ruby only has enough wrappers to make at most 75 dozen cupcakes. Ruby sells Nilla Sprinkles for $25 per dozen and Midnight Magic for $20 per dozen. Ruby wants to know how many dozens of Nilla Sprinkles and Midnight Magic cupcakes should be made in order to make as much money as possible. Let x = number of Nilla Sprinkles cupcakes to make for the week (in dozens) x2 = number of Midnight Magic cupcakes to make for the week (in dozens) a) Write the objective function for this problem. (You don't need to write the full model here, just the objective function) b) Write the constraint that makes sure we do not exceed the available supply of eggs. (You don't need to write the full model here, just the single constraint) Write the constraint that makes sure we do not exceed the total amount of cupcakes Ruby can make in a week. (You don't need to write the full model here, just the single constraint) c)

1. Ruby Flyer is a UD student who makes cupcakes in her spare time. She is famous for making 2 types of cupcakes: Nilla Sprinkles (vanilla) and Midnight Magic (chocolate). Both types require eggs in their recipes and Ruby just purchased 240 organic eggs from a local farm. According to the recipes, 3 eggs are required to make 1 dozen of Nilla Sprinkles cupcakes and 2 eggs are required to make 1 dozen of Midnight Magic cupcakes. Ruby only has enough wrappers to make at most 75 dozen cupcakes. Ruby sells Nilla Sprinkles for $25 per dozen and Midnight Magic for $20 per dozen. Ruby wants to know how many dozens of Nilla Sprinkles and Midnight Magic cupcakes should be made in order to make as much money as possible. Let x = number of Nilla Sprinkles cupcakes to make for the week (in dozens) x2 = number of Midnight Magic cupcakes to make for the week (in dozens) a) Write the objective function for this problem. (You don't need to write the full model here, just the objective function) b) Write the constraint that makes sure we do not exceed the available supply of eggs. (You don't need to write the full model here, just the single constraint) Write the constraint that makes sure we do not exceed the total amount of cupcakes Ruby can make in a week. (You don't need to write the full model here, just the single constraint) c)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 3EQ: A florist offers three sizes of flower arrangements containing roses, daisies, and chrysanthemums....
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1. Ruby Flyer is a UD student who makes cupcakes in her spare time. She is famous for making 2 types of cupcakes: Nilla Sprinkles (vanilla) and Midnight Magic (chocolate). Both types require eggs in their recipes and Ruby just purchased 240 organic eggs from a local farm. According to the recipes, 3 eggs are required to make 1 dozen of Nilla Sprinkles cupcakes and 2 eggs are required to make 1 dozen of Midnight Magic cupcakes. Ruby only has enough wrappers to make at most 75 dozen cupcakes. Ruby sells Nilla Sprinkles for S25 per dozen and Midnight Magic for $20 per dozen. Ruby wants to know how many dozens of Nilla Sprinkles and Midnight Magic cupcakes should be made in order to make as much money as possible. Let x = number of Nilla Sprinkles cupcakes to make for the week (in dozens) x2 = number of Midnight Magic cupcakes to make for the week (in dozens) a) Write the objective function for this problem. (You don't need to write the full model here, just the objective function) b) Write the constraint that makes sure we do not exceed the available supply of eggs. (You don't need to write the full model here, just the single constraint) Write the constraint that makes sure we do not exceed the total amount of cupcakes Ruby can make in a week. (You don't need to write the full model here, just the single constraint)
Transcribed Image Text:1. Ruby Flyer is a UD student who makes cupcakes in her spare time. She is famous for making 2 types of cupcakes: Nilla Sprinkles (vanilla) and Midnight Magic (chocolate). Both types require eggs in their recipes and Ruby just purchased 240 organic eggs from a local farm. According to the recipes, 3 eggs are required to make 1 dozen of Nilla Sprinkles cupcakes and 2 eggs are required to make 1 dozen of Midnight Magic cupcakes. Ruby only has enough wrappers to make at most 75 dozen cupcakes. Ruby sells Nilla Sprinkles for S25 per dozen and Midnight Magic for $20 per dozen. Ruby wants to know how many dozens of Nilla Sprinkles and Midnight Magic cupcakes should be made in order to make as much money as possible. Let x = number of Nilla Sprinkles cupcakes to make for the week (in dozens) x2 = number of Midnight Magic cupcakes to make for the week (in dozens) a) Write the objective function for this problem. (You don't need to write the full model here, just the objective function) b) Write the constraint that makes sure we do not exceed the available supply of eggs. (You don't need to write the full model here, just the single constraint) Write the constraint that makes sure we do not exceed the total amount of cupcakes Ruby can make in a week. (You don't need to write the full model here, just the single constraint)
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