101 Very Garlic Inc produces garlic powders in three Asian c

10.1. Very Garlic Inc. produces garlic powders in three Asian countries: China, India, and South Korea. The company ships garlic powders from its production facilities to four US warehouses (Seattle, New York, Phoenix, and Miami). The shipping costs per ton from each production facility to each warehouse are listed below. The capacity

Seattle New York Phoenix Miami

at China, India, and South Korea facilities are 100, 300, and 200 tons per month, respectively. The demand at Seattle, New York, Phoenix, and Miami are 150, 100, 200, and 150 tons, respectively. The goal is to minimize the total shipping cost to satisfy the demand at the warehouses. Formulate the problem as a linear program and solve it.

Let xij be the amount (in tons) of garlic powders to be shipped from production facility i to warehouse j. Let i = 1, 2, 3 to be China, India, and South Korea, respectively. Let j = 1, 2, 3, 4 to be Seattle, New York, Phoenix, and Miami, respectively.

10.1.a (0.5 pt) What is the objective function?

A) min x11 + x12 + x13 + x14 + x21 + x22 + x23 + x24 + x31 + x32 + x33 + x34

B) max x11 + x12 + x13 + x14 + x21 + x22 + x23 + x24 + x31 + x32 + x33 + x34

C) min 19x11 + 20x12 + 13x13 + 21x14 + 18x21 + 23x22 + 18x23 + 6x24 + 11x31 + 14x32 + 15x33 + 22x34

D) max 19x11 + 20x12 + 13x13 + 21x14 + 18x21 + 23x22 + 18x23 + 6x24 + 11x31 + 14x32 + 15x33 + 22x34

Very Garlic’s quantitative analyst formulates the problem as a linear program and gives the formulation to an intern to solve. The intern asks you to help him explain what the formulation means. He shows you the following equations.

x11 + x12 + x13 + x14 100 (1)

x21 + x22 + x23 + x24 300 (2)

x31 + x32 + x33 + x34 200 (3)

x11 + x21 + x31 = 150 (4)

x12 + x22 + x32 = 100 (5)

x13 + x23 + x33 = 200 (6)

x14 + x24 + x34 = 150 (7)

xij 0 for each i = 1, 2, 3; j = 1, 2, 3, 4 (8)

10.1.b (0.5 pt) Which equation ((1) - (7)) represent Phoenix’s demand constraint? (Enter a number between 1 and 7.)

10.1.c (0.5 pt) Which equation ((1) - (7)) represent Seattle’s demand constraint? (Enter a number between 1 and 7.)

10.1.d (0.5 pt) Which equation ((1) - (7)) represent New York’s demand constraint? (Enter a number between 1 and 7.)

10.1.e (0.5 pt) Which equation ((1) - (7)) represent Miami’s demand constraint? (Enter a number between 1 and 7.)

10.1.f (0.5 pt) Which equation ((1) - (7)) represent South Korea’s supply constraint? (Enter a number between 1 and 7.)

10.1.g (0.5 pt) Which equation ((1) - (7)) represent China’s supply constraint? (Enter a number between 1 and 7.)

10.1.h (0.5 pt) Which equation ((1) - (7)) represent India’s supply constraint? (Enter a number between 1 and 7.)

10.1.i (0.5 pt) Use Excel Solver to solve this problem and report the minimum total shipping cost.

Solution

10.1. a) option C

        b) 6

        c)4

        d)5

        e)7

        f)3

       g)1

        h)2