Let’s consider that the company manufactures x boxes of type A screws and y boxes of type B screws.
From the given information the below table is constructed:
From the data in the above table, the objective function for maximum profit Z = 100x + 170y
Subject to the constraints
2x + 8y ≤ 3600 ⇒ x + 4y ≤ 1800 … (i)
3x + 2y ≤ 3600 … (ii)
x ≥ 0, y ≥ 0 (non-negative constraints)
Therefore, the required LPP is
Maximize: Z = 100x + 170y
Subject to constraints,
x + 4y ≤ 1800, 3x + 2y ≤ 3600, x ≥ 0, y ≥ 0.
The objective function for maximum profit Z = 100x + 170y
Subject to constraints,
x + 4y ≤ 1800 …. (i)
3x + 2y ≤ 3600 … (ii)
x ≥ 0, y ≥ 0
Now, let’s construct a constrain table for the above
Table for (i)
Next, solving equations (i) and (ii), we get
x = 1080 and y = 180
It’s seen that OABC is the feasible region whose corner points are O(0, 0), A(1200, 0), B(1080, 180) and C(0, 450).
On evaluating the value of Z, we have
Form the table it’s seen that the maximum value of Z is 138600.
Therefore, the maximum profit of the function Z is 138600 at (1080, 180).