Robert is planning to spend the day baking c batches of cookies and b batches of brownies. He would like to maximize the total number of batches, c+b. He can bake a batch of cookies in 12 minutes and a batch of brownies in 30 minutes. Robert wants to spend at most 6 hours baking. He also wants to make sure the number of batches of brownies is within 2 of the number of batches of cookies. Create an inequality constraint for time (in hours) and two inequality constraints for the relative numbers of cookies and brownie batches.
Robert is planning to spend the day baking c batches of cookies and b batches of brownies. He would like to maximize the total number of batches, c+b. He can bake a batch of cookies in 12 minutes and a batch of brownies in 30 minutes. Robert wants to spend at most 6 hours baking. He also wants to make sure the number of batches of brownies is within 2 of the number of batches of cookies. Create an inequality constraint for time (in hours) and two inequality constraints for the relative numbers of cookies and brownie batches.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Robert is planning to spend the day baking c batches of cookies and b batches of
brownies. He would like to maximize the total number of batches, c+ b. He can bake a
batch of cookies in 12 minutes and a batch of brownies in 30 minutes. Robert wants to
spend at most 6 hours baking. He also wants to make sure the number of batches of
brownies is within 2 of the number of batches of cookies.
Create an inequality constraint for time (in hours) and two inequality constraints for the
relative numbers of cookies and brownie batches.
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Expert Solution
Inequality constraint for time
Let number of batches of cookies =c
and the number of batches of brownies=b
Total Number of batches = c+b
According to the question,
Robert has to maximize total number of batches, i.e. c+b
He takes 12 minutes in baking a batch of cookies and 30 minutes to bake a batch of brownies.
and he has maximum of 6 hours of baking
So inequality constraint for time is,
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