Question

Q1: A firm produces 3 products. These products are processed on 3 different machines. The time required to manufacture 1 unit of each of the 3 products and the daily capacity of the 3 machines are given in the table below:

Machine	Time per unit (mins)			Machine capacity (mins/day)
	Product 1	Product 2	Product 3
M1	2	3	2	440
M2	4	-	3	470
M3	2	5	-	430

It is required to determine the daily number of units to be manufactured for each product. The profit per unit for product 1, 2, and 3 is $4, $3, and $6 respectively. It is assumed that all the amounts produced are consumed in the market. Formulate the mathematical model for the problem.

Solution:

Answer 1

Since only the formulation is required, we will not solve the formulated LPP.

Let no. of product 1 be x, product 2 be y and product 3 be z

Total profit = 4*x + 3*y + 6*z

We have to maximize this profit

Hence, we get the objective function as:

Maximize Total Profit P = 4x + 3y + 6z

Total time required in Machine M1 = 2x + 3y + 2z

Total time available = 440 mins/ day

Hence, we get constraint as 2x + 3y + 2z <= 440

Similalrly for machine M2, 4x + 0y + 3z <= 470

For machine M3, 2x + 5y + 0z <= 430

Hence, we get formulation of mathematical model as

Maximize Total Profit P = 4x + 3y + 6z

Subject to Constraints:

2x + 3y + 2z <= 440

4x + 0y + 3z <= 470

2x + 5y + 0z <= 430

x, y, z >= 0..................Non-negativity constraint since no. of product scannot be negative

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