Aswad Al-Abyad, an ISE student, won a local talent competition, which entitled him to 50; 000 SAR. He is now planning to go on a two-month vacation trip to Europe during the coming summer vacation. He is planning to pack some items in the luggage, and buy some items in the foreign land. For the items that he packs, he is also considering the weight and size that he has to carry during the fights. Since he took a couple of courses in Operations Research, he plans to nd the optimal number of items from each category (A, B..., F) that he should pack. In order to build a mathematical model, he collected the following data:

	A	B	C	D	E	F
Weight per item	150	400	1000	100	800	2000
Volume per item	600	1800	2000	3000	1500	200
Unit Price in home country	140	340	1000	500	2000	100
Unit Price in foreign country	20	30	40	20	300	100
Required Items during vacation (min, max)	(16,24)	(8,12)	(3,5)	(6,14)	(17,23)	(9,11)

In the above table, the weight is expressed in gms, the volume is expressed in cc. In addition to that, the price in home country is expressed in SAR, while the price in foreign country is expressed in Euro. For example: Category A could represent t-shirt, and each item of A weighs 150 gms, takes 600 cc of space, costs 140 SAR in home country, costs 30 Euro in the foreign country. In addition to that, the total amount of items from A that will be enough for the entire vacation will be 16 to 24 units. In order to pack items he has the following restrictions:

R-(a): The total expenses of items that he buys in home country should not exceed 20; 000 SAR. R-(b): The total weight he likes to carry is 40 Kgs. R-(c): The total volume he likes to carry is 50; 000 cc. R-(d): The minimum requirements for items during the vacation can be satised by either purchasing at home or foreign country. R-(e): The maximum requirements for items during the vacation can be satised by either purchasing at home or foreign country. R-(f): A total of at-least 10 items should be packed. R-(g): If an item from C is packed, then an item from D should also be packed. R-(h): If items from B or E is packed, then items from C should not be packed. R-(i): If items from A and B are packed, then items from D should also be packed. R-(j): Items from F are allowed in the luggage only after paying an additional 100 SAR per item.

Answer the following questions: Q1. What are the possible decision variables that you can think of for the above model? Q2. Dene variables that capture number of items in each category purchased in the home country. Q3. Dene variables that capture whether an item is purchased or not in the home country. Q4. Connect the above two variables based on logical reasoning. Q5. Dene parameters for weight, volume, prices, and requirements. Use distinct name and consistent indices. Q6. Write the explicit mathematical model's constraints satisfying all the rules (R-(a) to R-(i)). Q7. Write the objective function that minimizes the overall cost of buying all items.

Q8. Dene a parameter that captures the additional cost dened in R-(j). Q9. Incorporate R-(j) into the previous model by appropriately modifying the objective function, and updating/adding constraints.

+ Note: The above questions are related. You can add new variables or parameters for the questions. Whenever a new parameter is used, it must be clearly dened. Whenever a new variable is used, it must be clearly dened and connected. Write an explicit constraint or objective function means: do NOT use summation ( P ) and enumeration (8) symbols. You should use the dened parameters and variables with explicit indices. The data/information given in this question is ctitious and for educational purpose only. 4