Q. 45.0( 3 Votes )

A company i

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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