Location Problem

Part A:

Consider the transportation data set for a distribution problem below.

From \ to	Dest 1	Dest 2	Dest 3	Dest 4	Total Supply
Plant 1	$14	$15	$12	$11	130
Plant 2	$10	$16	$7	$23	80
Plant 3	$19	$8	$12	$24	105
Total Demand	80	75	90	65

In this linear programming model, the objective function should be written as . . .

		Minimize x11 + x12 + x13 + x14 + x21 + x22 + x23 + x24 + x31 + x32 + x33 + x34
		Maximize 14x11 + 15x12 +12x13 + 11x14 + 10x21 + 16x22 + 7x23 + 23x24 + 19x31 + 8x32 + 12x33 + 24x34
		Minimize 14x11 + 15x12 +12x13 + 11x14 + 10x21 + 16x22 + 7x23 + 23x24 + 19x31 + 8x32 + 12x33 + 24x34
		Maximize x11 + x12 + x13 + x14 + x21 + x22 + x23 + x24 + x31 + x32 + x33 + x34

Part B:

Consider the transportation data set for a distribution problem below.

From \ to	Dest 1	Dest 2	Dest 3	Dest 4	Total Supply
Plant 1	$14	$15	$12	$11	130
Plant 2	$10	$16	$7	$23	80
Plant 3	$19	$8	$12	$24	105
Total Demand	80	75	90	65

Which of the following is true about the supply constraints in this problem? (choose all that apply)

		There are 3 supply constraints.
		One of the supply constraints is x21 + x22 + x23 + x24<= 80
		One of the supply constraints is x12 + x22 + x32 <= 90
		One of the supply constraints is x21 + x22 + x23 + x24 >=80
		One of the supply constraints is x12 + x22 + x32 = 90
		There are 4 supply constraints.

Part C:

Consider the transportation data set for a distribution problem below.

From \ to	Dest 1	Dest 2	Dest 3	Dest 4	Total Supply
Plant 1	$14	$15	$12	$11	130
Plant 2	$10	$16	$7	$23	80
Plant 3	$19	$8	$12	$24	105
Total Demand	80	75	90	65

Which of the following is true about the demand constraints in this problem? (choose all that apply)

		There are 4 demand constraints.
		There are 3 demand constraints.
		One of the demand constraints is x12 + x22 + x32 =75
		One of the demand constraints is x12 + x22 + x32 <= 90
		One of the demand constraints is x21 + x22 + x23 + x24 >=80
		One of the demand constraints is x21 + x22 + x23 + x24<= 80

Part D:

(True or False)

In addition to supply constraints and demand constraints, the model also consists of non-negativity constraints.

True

False

Part E:

From/To	Dest 1	Dest 2	Dest 3	Dest 4	Total Supply
Plant 1					120
Plant 2					90
Plant 3					105
Total Demand	75	80	90	65

After completing the northwest corner method with the transportation example above, indicate how many units (whole numbers) ship along each of these routes:

units should be shipped from plant 1 to destination 1,

units should be shipped from plant 2 to destination 2,

and units should be shipped from plant 3 to destination 4.

Part F:

Consider the transshipment costs per unit shipped below for this problem.

From/To	Dest 1	Dest 2	Dest 3	Dest 4	Total Supply
Plant 1	$10	$12	$8	$7	Unlimited
Plant 2	$5	$7	$9	$8	Unlimited
Plant 3	$8	$15	$20	$6	Unlimited
Total Demand	75	105	95	80

Find the lowest cost solution assuming each of the suppliers has an unlimited supply.

How many units (whole numbers) ship along each of these routes:

units should be shipped from plant 1 to destination 1,

units should be shipped from plant 2 to destination 2,

and units should be shipped from plant 3 to destination 4.

Part G

Consider the transshipment costs per unit shipped below for this problem.

From \ to	Dest 1	Dest 2
Plant 1	$46	$51
Plant 2	$35	$30
Plant 3	$63	$70

Consider this distribution plan below.

From \ to	Dest 1	Dest 2	Total Supply
Plant 1	30	10	40
Plant 2	20	60	80
Plant 3	30	5	35
Total Demand	80	75

What is the total cost (dollars) associated with this distribution plan? (round to a whole number)