Question

For this section, no need to solve the questions and submit answers Your company is a major distributor of coffee in the UAE. You can buy coffee from 5 roasters and distribute the coffee to three UAE cities (Al-Ain Abu Dhabi and Dubai). The monthly demand in the three cities is as follows: City Monthly Demand (tons) 1. Al-Ain 50 2- Abu Dhabi 120 3. Dubai 280 order to guarantee supplies from the five coffee roasters, you need to sign a monthly contract with fee. If you decide to sign a contract with a roaster, you need to pay the contract fee and then you need to pay for transportation cost of any coffee supplied from the roaster to the 3 cities. The production capacity of each roaster and their monthly fee are as follows: Roaster Monthly Supply (tons) Monthly Fee (contract) 75 5800 B 150 $1200 175 $1350 D 200 $1500 E 125 $1000 The transportation cost per ton of coffee from roasters to the 3 UAE cities is as follows: Roaster Al-Ain Abu Dhabi Dubai $5 SB 56 53 $6 57 $4 $9 96 D $8 SS $9 E 57 59 $2 Your company asked you to minimze the total monthly cost of coffee supply from the five roasters and distribution to the three UAE cities B Your company asked you to minimize the total monthly cost of coffee supply from the five roasters and distribution to the three UAE cities. 12. How many binary decision variables are needed for the formulation? (1 Point) O 15 20 Os 13. If Y is used to represent the binary decision variable, one of the following is the correct formulation for the constraint that represents the capacity of Roaster C: (1 Point) X1 + X2c +X30 - 175YC <= 0 Xc1 + Xc2-c3 <= 175 Xc1 + Xc2 +Xc3 - 1757€ <= 0 X16X2c +36 <= 175 14. One of the following is the correct formulation of the constraint that represents the demand in Al-Ain: (1 Point) O Xa1 + Xb1 +Xc1 + Xd1 + Xe1 <= 50 O X1a + X1b +X1C + X1d + X1e = 50 O Xa1 + Xb1 +Xc1 + Xd1 + Xe1 >= 50 O X1a + X1b +X1c + X1d + X1e >= 50 15. How many elements are needed in the Z-function to minimize both fixed costs of roasters and variable transportation costs from roasters to the three cities? (1 Point) O 20 08 15

Answer 1

Answer 12:

Based on the information given in the question, we can define the decision variables as mentioned below:

Let,

Xa1 = # Tons of coffee to be supplied from Roaster A to City 1

Xa2 = # Tons of coffee to be supplied from Roaster A to City 2

Xa3 = # Tons of coffee to be supplied from Roaster A to City 3

Xb1 = # Tons of coffee to be supplied from Roaster B to City 1

Xb2 = # Tons of coffee to be supplied from Roaster B to City 2

Xb3 = # Tons of coffee to be supplied from Roaster B to City 3

Xc1 = # Tons of coffee to be supplied from Roaster C to City 1

Xc2 = # Tons of coffee to be supplied from Roaster C to City 2

Xc3 = # Tons of coffee to be supplied from Roaster C to City 3

Xd1 = # Tons of coffee to be supplied from Roaster D to City 1

Xd2 = # Tons of coffee to be supplied from Roaster D to City 2

Xd3 = # Tons of coffee to be supplied from Roaster D to City 3

Xe1 = # Tons of coffee to be supplied from Roaster E to City 1

Xe2 = # Tons of coffee to be supplied from Roaster E to City 2

Xe3 = # Tons of coffee to be supplied from Roaster E to City 3

Thus, Xij = # Tons of Cofee to be supplied from Roaster 'i' to City 'j'

Moreover,

Ya = 1 if Roaster A is selected for supplying coffee, 0 otherwise

Yb = 1 if Roaster B is selected for supplying coffee, 0 otherwise

Yc = 1 if Roaster C is selected for supplying coffee, 0 otherwise

Yd = 1 if Roaster D is selected for supplying coffee, 0 otherwise

Ye = 1 if Roaster E is selected for supplying coffee, 0 otherwise

Thus, Yi = 1 if Roaster 'i' is selected for supplying coffee, 0 otherwise

Where, Xij ≥ 0 and Yi = {1 , 0}

Hence, we conclude that there are 5 binary decision variables needed for the formulation of the given question. (Option C or the Third Option)

Answer 13:

The supply constraint for Roaster 3:

Xc1 + Xc2 + Xc3 ≤ 175 Yc

∴ Xc1 + Xc2 + Xc3 - 175 Yc ≤ 0  (Option C or the Third Option)

Answer 14:

Demand Constraint for the City Al-Ain (i.e., City 1)

Xa1 + Xb1 + Xc1 + Xd1 + Xe1 ≥ 50 (Option C or the Third Option)

Answer 15:

Based on the decision variables decided in answer 12, there are total 20 elements (i.e., 15 Xij and 5 Yi) values needed in order to minimize the total of fixed and variable transportation costs from roasters to the three cities (Option A or the Third Option)

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