Question

Three different aeroplanes are to be assigned to carry three cargo consignments with a view to maximize profit. The profit matrix (in lakhs of ₹) is as follows : 

Aeroplanes	Cargo consignments
	C1	C2	C3
A1	1	4	5
A2	2	3	3
A3	3	1	2

How should the cargo consignments be assigned to the aeroplanes to maximize the profit? 

Answer 1

Given problem is of maximization Given matrix is 

	C1	C2	C3
A1	1	4	5
A2	2	3	3
A3	3	1	2

Above problem can be converted into minimization problem by subtracting each of the elements in the table from the largest element (5 here)
Maximum from the above matrix is 5. 
∴ Matrix for minimization problem is 

	C1	C2	C3
A1	4	1	0
A2	3	2	2
A3	2	4	3

Subtracting row minimum from each row 

	C1	C2	C3
A1	4	1	0
A2	1	0	0
A3	0	2	1

 Minimum in each column is zero 
∴ There is no change in the above matrix. 
∴ Allocation is 

∴ Assignment is A₁ → C₃ , A₂ → C₂, A₃ → C1 

∴ Maximum profit is = 5+3+3 
                                  = 11 lakhs