New Year Problem
Today is December 31, 2015 and Mark has plans of having a New Year Party at his place which will start at 10:00 PM.
So at 8:00 AM, He then thought of the food to serve. He chooses between ordering the food or cooking the food himself.
Mark has a car. 0.5 liter of gasoline can take him 5 km. 1 liter costs him $4.
He uses the car to go to his chosen restaurant or grocery. (He doesn't commute or walk). He can't choose other places to buy from that is not stated below.
{Assume that he walked to a gasoline station, bought gasoline there, and returned home.}
If he choose to order food then he will have to choose from which restaurant to order from:
Niall's Restaurant: [5 km from Mark's house]
-
30 pieces of Fried Chicken ($60)
-
2 trays of Carbonara ($70)
-
4 boxes of Pizza ($52)
-
30 pieces of Brownies ($45)
Oliver's Restaurant: [4.5 km from Mark's house]
-
30 pieces of Fried Chicken ($75)
-
2 trays of Carbonara ($60)
-
4 boxes of Pizza ($48)
-
30 pieces of Brownies ($39)
But, if he will cook the food himself then he would have to buy the ingredients and choose from which grocery to buy from:
Patrick's Grocery [7 km from Mark's house]
-
30 pieces of Chicken ($30)
-
2 pieces of Carbonara Pack which makes 1 tray each ($50)
-
4 pieces of Pizza Pack which makes 1 box each ($40)
-
3 pieces of Brownie Pack which makes 10 brownies each ($15)
Queenie's Grocery [7.1 km from Mark's house]
-
30 pieces of Chicken ($27)
-
2 pieces of Carbonara Pack which makes 1 tray each ($52)
-
4 pieces of Pizza Pack which makes 1 box each ($44)
-
3 pieces of Brownie Pack which makes 10 brownies each ($12)
[Assume that a _ Pack is a complete pack filled with ingredients in making that _ __. For example, a Carbonara Pack has carbonara sauce, pasta, cheese, etc. in it.]
[All options result in equal amount of food]
{Remember: after ordering or buying the food from the restaurant or grocery, Mark has to return to his house.}
Mark only needs the cheapest option.
Which option will Mark choose?
{Image from dir.coolclips.com}
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
First of all, I'll know how many liters are needed in order to travel for 1 km. So, 0.5 liters = 5 km, then, 0.1 liters = 1 km. 1 liter costs $4. So, 0.1 liters costs $0.40.
$0.40 = 1 km = 0.1 liters of gasoline
Then I'll total the prices for each option:
Niall's Restaurant:
$60 + $70 + $52 + $45 = $227
Oliver's Restaurant:
$75 + $60 + $48 + $39 = $222
Patrick's Grocery:
$30 + $50 + $40 + $15 = $135
Queenie's Grocery:
$27 + $52 + $44 + $12 = $135
The prices from the gasoline:
Niall's Restaurant:
5 km x 2 = 10 km x $0.40 = $4
Oliver's Restaurant:
4.5 km x 2 = 9 km x $0.40 = $3.6
Patrick's Grocery:
7 km x 2 = 14 km x $0.40 = $5.6
Queenie's Grocery:
7.1 km x 2 = 14.2 km x $0.40 = $5.68
Then, add all the costs:
Niall's Restaurant:
$227 + $4 = $231
Oliver's Restaurant:
$222 + $3.6 = $225.6
Patrick's Grocery:
$135 + $5.6 = $140.6
Queenie's Grocery:
$135 + $5.68 = $140.68
The cheapest option is from Patrick's Grocery.
Hence, the answer is Patrick's Grocery.