Jenny's Bakery: The Real World Problem
The real world problem that we will use is:
Jenny’s bakery makes two types of cakes:
Angel food cake which sells for $25
Red Velvet Cake which sells for $35
Both cakes are the same size, but the decorating and assembly time required for the angel food cake is 2 hours, while the time for the red velvet cake is 3 hours. There are 450 hours of labor available for production. How many of each cake should Jenny make to maximize revenue? For this problem we will use linear optimization, which is a method for finding the maximum or minimum of a function over a given system of inequalities, with each representing a constraint. An example of a constraint would be how much you spend, make, number of employees, space and time. In the real world problem that we are using, the constraints would be 450 hours of labor available for production. …show more content…
Your two variables are the two options given to you in the problem, so the options that we have are angel food cake and red velvet cake. Next with your constraint, which I had said was 450 hours of labor available for production, you need to write an inequality. For all of our inequalities in linear optimization, you will use a greater than or less than sign, which means all of your lines will be solid. Going back to your two variables, you use these and your constraint to write the inequality, which with this problem you will only have one inequality. Since 450 hours is the maximum amount of hours for production, your inequality should start with 450 is greater than or equal to your inequality. Now take your two variables and add in their amount of numbers that was set to them from the problem. X will have 2 hours and Y will have 3 hours, you take these two variables and add them to 450 is greater than or equal to. Now you have a inequality of 450 is greater than or equal to 2X plus
Jenny’s bakery makes two types of cakes:
Angel food cake which sells for $25
Red Velvet Cake which sells for $35
Both cakes are the same size, but the decorating and assembly time required for the angel food cake is 2 hours, while the time for the red velvet cake is 3 hours. There are 450 hours of labor available for production. How many of each cake should Jenny make to maximize revenue? For this problem we will use linear optimization, which is a method for finding the maximum or minimum of a function over a given system of inequalities, with each representing a constraint. An example of a constraint would be how much you spend, make, number of employees, space and time. In the real world problem that we are using, the constraints would be 450 hours of labor available for production. …show more content…
Your two variables are the two options given to you in the problem, so the options that we have are angel food cake and red velvet cake. Next with your constraint, which I had said was 450 hours of labor available for production, you need to write an inequality. For all of our inequalities in linear optimization, you will use a greater than or less than sign, which means all of your lines will be solid. Going back to your two variables, you use these and your constraint to write the inequality, which with this problem you will only have one inequality. Since 450 hours is the maximum amount of hours for production, your inequality should start with 450 is greater than or equal to your inequality. Now take your two variables and add in their amount of numbers that was set to them from the problem. X will have 2 hours and Y will have 3 hours, you take these two variables and add them to 450 is greater than or equal to. Now you have a inequality of 450 is greater than or equal to 2X plus