Question

A ferry service operates between the mainland and the island of Deltar, carrying vehicles and

people. There is a scale of charges for the crossing by car and minibus.


Car: $50 for a car and driver, plus a charge of $12 for each additional person. The maximum

number of people allowed in a car is four. There is a 10% discount on the total cost for cars

carrying at least three people (including the driver).


Minibus: $242 for a minibus. The maximum number of people allowed in a minibus is 10 people

including the driver. There is a $30 discount for a minibus carrying exactly 10 people.


A bowling club with 17 members wishes to travel to Deltar for a tournament. Each of the

members is able to drive a car and each is able to drive a minibus.


What is the lowest cost for the bowling club members to make the crossing on the ferry?


A $344.00

B $354.60

C $356.00

D $359.60

Answer 1

D $359.60

Explanation:

We start by calculating the per-person cost for a full car and for a full minibus.

For a car with 4 members, the cost per person is:

`c_(c4)=(0.9\cdot (50+12*3))/(4)=(77.4)/(4)=19.35`

A car with 3 members will cost per person:

`c_(c3)=(0.9\cdot (50+12*2))/(3)=(74)/(3)=24.67`

For the minibus (10 people) the cost per person is:

`c_m=(242-30)/(10)=(212)/(10)=21.20`

The full car is cheaper per person, but if we fill 4 cars with 4 people each, there is one person left, and it will cost an additional $50.

This option will cost:

`C_1=4\cdot(4c_c)+c_1=4*4*19.35+50=309.60+50=359.60`

As a 3-person car is considered full and have discount, we can arrange 2 cars with 4 people (8 people total) and 3 cars with 3 people (9 people total), and then complete the team of 17.

This would have the cost:

`C_2=2*(4c_(c4))+3*(3c_(c3))=2*(4*19.35)+3*(3*24.67)=154.8+222.03=376.83`

The third option, would be use the minibus (10 people) and 2 cars: one with 4 people and the other with 3. This would have a cost of:

`C_3=10*c_m+4*c_(c4)+3*c_(c3)=212+4*19.35+3*24.67\\\\C_3=212+77.4+74=363.4`

As this are the best options, the lowest cost is $359.60.