A furniture manufacturer produces two types of chairs: A and B. Chair A requires 2 hours of cutting, 1 hour of assembling, and 3 hours of finishing. Chair B requires 1 hour of cutting, 2 hours of assembling, and 1 hour of finishing. If the manufacturer has 20 hours of cutting, 12 hours of assembling, and 30 hours of finishing available each day, how many chairs of each type should be produced to maximize profit, if the profit on chair A is Rs. 30 and on chair B is Rs. 25?

Let x be the number of chairs of type A produced. Let y be the number of chairs of type B produced.

The objective function, to be maximized, is given by:

Z = 30x + 25y

The constraints are:

2x + y <= 20 (cutting) x + 2y <= 12 (assembling) 3x + y <= 30 (finishing) x >= 0, y >= 0

Solving the above system of linear inequalities graphically, we get the feasible region, as shown in the figure below.

Graph is missing

The corner points of the feasible region are (0,0), (0,10), (6,0), and (8,2).

Computing the value of the objective function at each corner point, we get:

Z(0,0) = 0 Z(0,10) = 250 Z(6,0) = 180 Z(8,2) = 260

Therefore, the maximum profit of Rs. 260 is obtained by producing 8 chairs of type A and 2 chairs of type B.

Answer: 8 chairs of type A and 2 chairs of type B should be produced to maximize profit.