A company is making two products A and B. The cost of producing one unit of products A and B are Rs 60 and Rs 80 respectively. As per the agreement, the company has to supply at least 200 units of product B to its regular customers. One unit of product A requires one machine hour whereas product B has machine hours available abundantly within the company. Total machine hours available for product A are 400 hours. One unit of each product A and B requires one labour hour each and total of 500 labour hours are available. The company wants to minimize the cost of production by satisfying the given requirements. Formulate the problem as a LPP.

Asked by Sakshi | 1 year ago | 136

Now, let x and y be the required production of products A and B.

Given:

Profit on one unit of product A is = Rs 60

So, profit on x unit of product A = 60x

Profit on one unit of product B is = Rs 80

So, profit on x unit of product B = 80y

Let total profit be ‘Z’

So, Z = 60x + 80y

First constraint:

Given, Minimum supply of product B is 200

So, y ≥ 200

Second constraint:

Given:

Production of one unit of product A requires 1hour per week of machine hours.

So, x units of product A requires 1x hour per week and

Total machine hours available for product A is 400hours,

So, x ≤ 400

Third constraint:

Given:

Production of one unit of product A requires 1hour per week of labour hours.

Production of one unit of product B requires 1hour per week of labour hours.

So, x units of product A requires 1x hour per week and

y units of product B requires 1x hour per week.

Total labour hours available is 500hours,

So, x + y ≤ 500

Hence, the required mathematical formulation of linear programming is:

Minimize Z = 60x + 80y

Subject to

x ≤ 400

x + y ≤ 500

Where, x, y ≥ 0

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