Numericals on Maximization Assignment Model

(Maximization)

1.         A manufacturer has 5 machines and 5 workers working. The output for worker machine combination is given.

(i)       Find worker machine combination that maximizes total output

(ii)      If profit per unit is Rs. 10/-. Find total profit.

(Ans :  W₁ ® 1, W₂ ® 5, W₃ ® 3, W₄ ® 4, W₅ ® 2; Total Output = 160 units, Total profit = Rs. 1600)

2.         Four machines can do 4 jobs. The output per machine in units is given below. Determine the job machine combination for maximum profit.

(Ans :  M₁ ® 1, M₂ ® 2, M₃ ® 4, M₄ ® 3 OR M₁ ® 3, M₂ ® 2, M₃ ® 4, M₄ ® 1)

3.         5 salesman are to be assigned 5 cities based on past performance data and following table sowing annual sales (in Rs. Lakhs). Find optimum assignment

 (Ans :  S₁ ® A, S₂ ® B, S₃ ® E, S₄ ® D, S₅ ® C; Sales = 26 + 27 + 30 + 30 + 25 = 138 lakhs)

4.         A five star hotel which has 4 banquet halls was used for functions. The halls are of same but with varying facilities. 4 parties approached to a hall for the function on same day. These parties were told that the first choice would cost Rs. 10,000 for the day. They were told to indicate the 2^nd, 3^rd & 4^th preferences and the price they were willing to pay the two parties A & D told that they were not interested in halls 3 and 4. The following table shows preference wise income details. What would be the optimal assignment to maximize the total revenue ? (Figures in 1000)

          (Ans :  A ® 2, B ® 3, C ® 4, D ® 1; Revenue (1000) = 9 + 8 + 8 +  10 = 35)