March 28th, 2014
Grilled Cheese Problem
Problem Solving 007
In our problem for the week of special topics were are given a problem regarding achieving a best time to make grilled cheeses in a efficient manner in the shortest amount of time. The problem states; You need to make five grilled cheese sandwiches. You have a grill that is large enough to toast two sandwiches at a time. The sandwiches must be toasted one minute on each side. It takes 3 seconds to flip a sandwich and 5 seconds to take one off or put one on the grill. What is the shortest time needed to toast all five sandwiches? So with the information given we can conclude that the sandwiches have to be toasted at least 5 mins so it is obvious we cant get anything lower then 5 mins. Next we make an assumption that we can flip two sandwiches at the same time as well as take off and put on two sandwiches as well as take off two sandwiches all simultaneously. So the best way to solve this problem would be to first simpify the problem so that it is easier to see the soultion. So I decided to label the grill cheeses. Each side is denoted by A, B,C, D, E. So assuming the time starts for for the countdown when the two sandwiches are put on the Grill. Step 1: A B toasted one side 1 min =1min Step 2: Now Remove B and put C 5sec+5sec+3sec=13 sec( for removing B 5 sec + put C 5 sec+ flip A 3sec) Step 3 A C toasted on grill 1 min =1min Step 4: Now Remove A(completed) and put D 5sec+5sec+3sec=13 sec ( for removing A 5 sec + put C 5 sec+ flip C 3sec) Step 5 C D toasted on grill 1min =1min Step 6 (remove C(completed) ,put E, flip D) 5sec+5sec+3sec=13 sec Step 7 D E toasted on grill toasted 1 min =1min Step 8 remove D(completed), put B , flip E 5sec+5sec+3sec=13 sec Step 9 B E toasted on Grill 1 min =1min TOTAL = 5 min. 52 sec
The process stops as all the five sandwiches are toasted, time is not counted for not taking the A and E off the grill. So the shortest time achievable...
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