Given information can be tabulated as below:

Let the required product of product A and B be x and y units respectively.

Given, labour cost and raw material cost of one unit of product A is Rs 16 and Rs 4, so total cost of product A is Rs 16 + Rs 4 = Rs 20

And given selling price of 1 unit of product A is Rs 25,

So, profit on one unit of product

A = 25 - 20 = Rs 5

Again, given labour cost and raw material cost of one unit of product B is Rs 20 and Rs 4 So, that cost of product B is Rs 20 + Rs 4 = Rs 24

And given selling price of 1 unit of product B is Rs 30

So, profit on one unit of product B = 30 - 24 = Rs 6

Hence, profits on x unit of product A and y units of product B are Rs 5x and Rs 6y respectively.

Let Z be the total profit, so,

Z = 5x + 6y

Given, production of one unit of product A and B need to process for 3 and 4 hours respectively in department 1, so production of x units of product A and y units of product B need to process for 3x and 4y hours respectively in Department 1. But total capacity of Department 1 is 130 hours,

So, 3x + 2y ≤ 130 (First constraint)

Given, production of one unit of product. A and B need to process for 4 and 6 hours respectively in department 2, so production of x units of product A and y units of product B need to process for 4x and 6y hours respectively in Department 2 but total capacity of Department 2 is 260 hours

So, 4x + 6y ≤ 260 (Second constraint)

Hence, mathematical formulation of LPP is,

Find x and y which

Maximize Z = 5x + 6y

Subject to constraint,

3x + 2y ≤ 130,

4x + 6y ≤ 260

x, y ≥ 0 [Since production cannot be less than zero]