(i) Variables:
Let x1 and x2 denote the two types products A and B respectively.
(ii) Objective function:
Profit on x1 units of type A product = 30x1
Profit on x2 units of type B product = 40x2
Total profit = 30x1 + 40x2
Let Z = 30x1 + 40x2, which is the objective function.
Since the profit is to be maximized, we have to maximize Z = 30x1 + 40x2
(iii) Constraints:
60x1 + 120x2 ≤ 12,000
8x1 + 5x2 ≤ 600
3x1 + 4x2 ≤ 500
(iv) Non-negative constraints:
Since the number of products on type A and type B are non-negative, we have x1, x2 ≥ 0
Thus, the mathematical formulation of the LPP is
Maximize Z = 30x1 + 40x2
Subject to the constraints,
60x1 + 120x2 ≤ 12,000
8x1 + 5x2 ≤ 600
3x1 + 4x2 ≤ 500
x1, x2 ≥ 0