(i) Variables:
Let x1 and x2 denotes the number of pens in type A and type B.
(ii) Objective function:
Profit on x1 pens in type A is = 5x1
Profit on x2 pens in type B is = 3x2
Total profit = 5x1 + 3x2
Let Z = 5x1 + 3x2, which is the objective function.
Since the B total profit is to be maximized, we have to maximize Z = 5x1 + 3x2
(iii) Constraints:
Raw materials required for each pen A is twice as that of pen B.
i.e., for pen A raw material required is 2x1 and for B is x2.
Raw material is sufficient only for 1000 pens per day
∴ 2x1 + x2 ≤ 1000
Pen A requires 400 clips per day
∴ x1 ≤ 400
Pen B requires 700 clips per day
∴ x2 ≤ 700
(iv) Non-negative restriction:
Since the number of pens is non-negative, we have x1 > 0, x2 > 0.
Thus, the mathematical formulation of the LPP is
Maximize Z = 5x1 + 3x2
Subj ect to the constrains
2x1 + x2 ≤ 1000, x1 ≤ 400, x2 ≤ 700, x1, x2 ≥ 0