Question

Which statement would justify selecting plan B instead of plan A?Plan A: C = 30dPlan B: C = 25d + 15

Answer 1

We have two rental car plans.

We have to compare them to find the one that offers the minimum cost.

Plan A has no fixed fee but has a cost of $30 per day:

`C=30d`

Plan B has a fixed fee of $15 and a cost per day of $25:

`C=25d+15`

We expect the plan A to have a smaller cost for few days, while plan B becomes more convenient when we increase the number of days.

We can calculate the break even point when both costs are the same:

`\begin{gathered} C_A=C_B \\ 30d=25d+15 \\ 30d-25d=15 \\ 5d=15 \\ d=(15)/(3) \\ d=5 \end{gathered}`

Then, we know that for less than 5 days, Plan A is more convenient.

For more than 5 days, Plan B is more convenient.

For exactly 5 days, the decision is indifferent as both plans will have the same total cost.

Answer: The only statement that would justify selecting Plan B instead of A is if Marcus rents a car for 5 days.