A factory produces two products, X and Y. The profit per unit of X is Rs. 4 and the profit per unit of Y is Rs. 5. The factory has two machines, A and B, which can be used to produce both products. Machine A can produce 6 units of X or 5 units of Y per hour, while machine B can produce 5 units of X or 6 units of Y per hour. If machine A is available for 48 hours and machine B is available for 54 hours, what is the maximum profit that can be earned?

We can set up the following linear programming problem:

Maximize Z = 4X + 5Y
Subject to:
6X + 5Y ≤ 48(6) (Machine A availability)
5X + 6Y ≤ 54(5) (Machine B availability)
X, Y ≥ 0

Solving this problem, we get the optimal production mix to be X = 6 units and Y = 6 units, with a maximum profit of Z = 4(6) + 5(6) = Rs. 42 per hour. Therefore, the total maximum profit that can be earned in 48+54=102 hours is Rs. 42*102 = Rs. 4,284. However, we are asked for the maximum profit that can be earned in the given time period, which is 48+54=102 hours. Therefore, the answer is (a) Rs. 792.