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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter5: Linear Inequalities
Section5.6: Graphing Ineualities In Two Variables
Problem 29PPS
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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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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. hp %23 %24 & 3. 4. 7 e r t. y <6
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

12 minutes=15hour and 30 minutes=12hour

So inequality constraint for time is,

15c+12b62c+5b60

 

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