Answer :

The given data can be shown in a table as follows:

Let production of product A be x units and of be B y units.

Given,

Profit on 1 unit of product A = Rs.60

Profit on 1 unit of product B = Rs.80

So, profit on x units of A and y units of B is 60x and 80y respectively.

Let z = total profit,

So, we have

z = 60x + 80y

Given, a minimum supply of product B is 200

So, y ≥ 200 (First constraint)

Given that, production of one unit of product A requires 1 hour of machine hours, so x units of product A require x hours but total machine time available for product A is 400 hours

So, x ≤ 400 (Second constraint)

Given, each unit of product A and B requires one hour of labour hour, so x units of product A require x hours and y units of product B require y hours of labour hours, but total labour hours available is 500 so

x + y ≤ 500 (Third constraint)

Hence, mathematical formulation of LPP is,

Find x and y which

Minimize z = 60x + 80y

Subject to constraints,

y ≥ 200

x ≤ 400

x + y ≤ 500

and also, as production cannot be less than zero, so x, y ≥ 0

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