Q1:

A company has three plants producing automobile parts that are to be shipped to four distribution centers. Each plant produces 30 shipments per month. Distribution centers 1, 2, 3, and 4 needs to receive 15, 25, 40, and 10 shipments per month, respectively. The route is unavailable from plant 2 to distribution center 3. The shipping cost per shipment from each plant to each distribution center is given in the following table:

	Distrib1	Distrib2	Distrib3	Distrib4
Plant1	5	7	7	10
Plant2	3	5	NA	6
Plant3	9	12	11	4

a) What is the optimal objective function value?

Select one:

a. 540

b. 555

c. 590

d. 550

e. 530

f. 580

g. 570

Q2:

Consider the following sensitivity report.

	Changing Cells
		Final	Reduced	Objective	Allowable	Allowable
Cell	Name	Value	Cost	Coeff.	Increase	Decrease
$B$4	Number to make: X1	7.5	2	7	1.54	2
$C$4	Number to make: X2	5.4	4	6	2	1.5
$D$4	Number to make: X3	7	2	7.5	4	1.5
	Constraints
		Final	Shadow	Constraint	Allowable	Allowable
Cell	Name	Value	Price	R.H.Side	Increase	Decrease
$D$8	Constraint1	43	0	55	1e+30	6
$D$9	Constraint2	132	2.5	135	42	12
$D$10	Constraint3	28	4.5	135	36	2

What is the smallest value of the objective function coefficient X3 can assume without changing the optimal solution?

Q3:

A basic feasible solution to a transportation problem satisfies the following conditions:

Select one or more:

a. The non-negativity constraints are satisfied

b. The allocations are independent and do not form a loop.

c. The row column (supply-demand) constraints are satisfied.

d. All the reduced costs of unallocated cells must be non-negative.

e. Allocated cells which are in the path of loop, but not corner cells, will not be considered in calculations.

f. There are exactly +-1 allocations where is number rows while is number of columns.

g. There cannot be 3 or more adjacent allocated cells in a row/column in the path of loop.