Let x and y be the number of pieces of type A and B manufactured per week respectively. If Z be the profit then,
Objective function, Z = 80x + 120y ...(i)
We have to maximize Z, subject to the constraints
9x + 12y ≤ 180
3x + 4y ≤ 60 ...(ii)
x + 3y ≤ 30 ...(iii)
x ≥ 0, y ≥ 0 ...(iv)
The graph of constraints are drawn and feasible region OABC is obtained, which is bounded having corner points O (0, 0), A(20, 0), B (12, 6) and C (0, 10)
Now the value of objective function is obtained at corner points as
Hence, the company will get the maximum profit of Rs 1,680 by making 12 pieces of type A and 6 pieces of type B of teaching aid.