A manufacturing firm produces two types of gadgets A and B, which are first processed in the foundry and then sent to the machine shop for finishing. The number of man-hours of labour required in each shop for production of A and B and the number of man-hours available for the firm is as follows :
|Time available (hour)||60||35|
Profit on the sale of A is ₹ 30 and B is ₹ 20 per units. Formulate the LPP to have maximum profit.
Let the number of gadgets A produced by the firm be x and the number of gadgets B produced by the firm be y.
The profit on the sale of A is ₹ 30 per unit and on the sale of B is ₹ 20 per unit.
∴ total profit is z = 30x + 20y
This is a linear function that is to be maximized. Hence it is the objective function. The constraints are as per the following table:
|Gadgets||Foundry||Machine shop||Total available Time (in hour)|
From the table total man-hours of labour required for x units of gadget A and y units of gadget B in foundry is (10x + 6y) hours and total man-hours of labour required in machine shop is (5x + 4y) hours.
Since the maximum time available in foundry and machine shops are 60 hours and 35 hours respectively. Therefore, the constraints are 10x + 6y ≤ 60, 5x + 4y ≤ 35.
Since, x and y cannot be negative, we have x ≥ 0, y ≥ 0. Hence, the given LPP can be formulated as:
Maximize z = 30x + 20y, subject to
10x + 6y ≤ 60,
5x + 4y ≤ 35,
x ≥ 0, y ≥ 0