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 M_{1}. So, x units of A, y units of B and z units of C need 4x, 3y and 5z minutes. Maximum capacity on machine M_{1} 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 M_{2}. So, x units of A, y units of B and z units of C require 2x, 2y and 4z minutes. Maximum capacity on machine M_{2} 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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