Q. 94.7( 3 Votes )

A firm manu

Answer :

The given data can be formulated in a table as below.



Let, required production of product A, B and C be x, y and z units respectively.


Given, profit on one unit of product A, B and C are Rs 3, and Rs 2, Rs 4.


So, profit on x, y, z units of A, B, C Rs 3x, Rs 2y, Rs 4z.


Let U be the total profit, so


U = 3x + 2y + 4z


Given, one unit of product A, B and C requires 4, 3 and 5 minutes on machine M1. So, x units of A, y units of B and z units of C need 4x, 3y and 5z minutes. Maximum capacity on machine M1 is 2000 minutes, so,


4x + 3y + 5z ≤ 200 0 (First constraint)


Given, one unit of product A, B and C requires 2, 2 and 4 minutes on machine M2. So, x units of A, y units of B and z units of C require 2x, 2y and 4z minutes. Maximum capacity on machine M2 is 2500 minutes, so,


2x + 2y + 4z ≤ 250 0 (Second constraint)


Also, given that firm must manufacture more than 100 A’s, 200 B’s, 50 C’s also not more than 150 A’s, so,


100 ≤ x ≤ 150,


y ≥ 200 (Other constraints)


z ≥ 50


Hence, mathematical formulation of LPP is:


Find x, y and z which maximize U = 3x + 2y + 4z


Subject of constraints,


4x + 3y + 5z ≤ 2000


2x + 2y + 4z ≤ 2500


100 ≤ x ≤ 150,


y ≥ 200


z ≥ 50


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

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