Question

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.

Answer 1

Answer:12c + 30b ≤ 360

Explanation:

Your math problem requires us to convert the word problem into math before we can solve the math. So let's try to do that first.

First, let's make a math equation to represent the amount of time.

The amount of time to bake "c" batches of cookies = (# of minutes per batch) x (# of batches) = 12 x c = 12c

Similarly for the amount of time to bake "b" batches of brownies = (# of minutes per batch) x (# of batches) = 30 x b = 30b

This is going to look like a format of:

(amount of time to bake cookies) + (amount of time to bake brownies) ≤ (total amount of time)

This person wants the (total amount of time) to be "at most 6 hours" but we can't just put "6" as our number because the other amounts of time are in "minutes".

6 hours * 60 minutes in an hour = 360 minutes

So our first equation becomes:

12c + 30b ≤ 360