30 points] When you prepared for this exam, you knew that there are 7 types of q

Question

30 points] When you prepared for this exam, you knew that there are 7 types of ques ions. In one dream, you successfully guessed the four types of this exam. Imagine another situation instead of the knapsack policy on what to bring. In this situation, you are only allowed to bring an 8X11 cheat sheet (one sided). The area and time needed to write down the content in the cheat sheet for each type of question can be found in the following Table. In addition, you have another option, that is to memorize the content of any type of question. But to memorize, it takes more time, which also can found in the table. The zeted scores for each type by using the two different options are different and shown r: the following table Type of sestions Area Needed (in 2) Time to Write Down (minute) Time to learn and memorize (minute) 26 Shortest Path CPM ILP Direct Search 35 15 45 30 30 50 23 80 21 25 25 20 30 20 29 35 15 Expected Score (using cheat sheet)25 Expected Score (memorizing) 29 Right before you start the preparation, your best friend throws a surprise party you can impossibly resist. After a fantastic party, you only have 2.5 hours to prepare. Please formulate an optimization model to help yourself.

Explanation / Answer

Formulation of LPP

Let

x11 = number of questions of ‘shortest path’ to be written on the cheat sheet,

x12 = number of questions of ‘shortest path’ to be memorised,

x21 = number of questions of ‘CPM’ to be written on the cheat sheet,

x22 = number of questions of ‘CPM’ to be memorised,

x31 = number of questions of ‘ILP’ to be written on the cheat sheet,

x32 = number of questions of ‘ILP’ to be memorised,

x41 = number of questions of ‘Direct Search’ to be written on the cheat sheet,

x42 = number of questions of ‘Direct Search’ to be memorized.

Then, the LPP would be:

Max Z = 25x11 + 29x12 + 15x21 + 20x22 + 25x31 + 30x32 + 25x41 + 20x42 [objective function on score maximisation]

Subject to

35x11 + 45x21 + 30x31 + 30x41 88 [sheet area in inch2]

15x11 + 26x12 + 29x21 + 35x22 + 50x31 + 80x32 + 23x41 + 21x42 150 [available time in minutes]

xij 0 for i = 1, 2, 3, 4 and j = 1, 2.

DONE

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