Question

The Peace River Sate Designated Paddle Trail is 67 miles long. Julia is planning on renting a canoe for a canoe trip on the Peace River Paddle Trail. The canoe outfitter charges $90 to transport the canoe and supplies to the acess point. The outfitter charges $2.50 for each mile of the trail that Julia plans to travel. To plan her budget Julia used the function C (m)=2.5m +90 where C is the cost in dollars and M is the number of miles she travels. Select all constraints for the context

m ≥ 0
m ≤ 67
m ≤ 90
C ≥ 0
C ≥ 90
C ≤ 257.5

Answer 1

• m ≥ 0
• m ≤ 67
• C ≥ 90
• C ≤ 257.5

Explanation:

Julia is using the cost function C(m) = 2.5m +90 where she expects m to be at most 67 miles. You want to identify the constraints on C and 'm' in the context of Julia's travels.

Domain

The value of m cannot be less than zero, and seems to be limited to 67 in this context. That is, m is subject to the constraints ...

0 ≤ m ≤ 67

Range

Those values of m will give values of C in the range ...

C(0) = 2.5·0 +90 = 90

C(67) = 2.5·67 +90 = 257.50

Thus, C is subject to the constraints ...

90 ≤ C ≤ 257.50