Question

Anita Electric Company produces two
products P1 and P2. Products are produced
and sold on a weekly basis. The weekly
production cannot exceed 25 for product
P1 and 35 for product P2 because of
limited available facilities. The company
employs a total of 60 workers. Product P1
requires 2 man-weeks of labour, while P2
requires one man-week of labour. The
profit margin on P1 is Rs. 60 and on P2 is
Rs. 40. Formulate this problem as an LP
problem​

Answer 1

The company employs a total of 60 workers. Product P1

employs a total of 60 workers. Product P1requires 2 man-weeks of labour, while P2

employs a total of 60 workers. Product P1requires 2 man-weeks of labour, while P2requires one man-week of labour. The

employs a total of 60 workers. Product P1requires 2 man-weeks of labour, while P2requires one man-week of labour. Theprofit margin on P1 is Rs. 60 and on P2 is

employs a total of 60 workers. Product P1requires 2 man-weeks of labour, while P2requires one man-week of labour. Theprofit margin on P1 is Rs. 60 and on P2 isRs. 40. Formulate this problem as an LP

employs a total of 60 workers. Product P1requires 2 man-weeks of labour, while P2requires one man-week of labour. Theprofit margin on P1 is Rs. 60 and on P2 isRs. 40. Formulate this problem as an LPproblem

Answer 2

Let:

x1 = the number of units of product P1 produced in a week

x2 = the number of units of product P2 produced in a week

Objective:

Maximize profit = 60x1 + 40x2

Constraints:

Production constraint for P1: x1 ≤ 25

Production constraint for P2: x2 ≤ 35

Labor constraint: 2x1 + x2 ≤ 60

Non-negative variables:

x1, x2 ≥ 0

The LP problem can be written as:

Maximize:

Z = 60x1 + 40x2

Subject to:

x1 ≤ 25

x2 ≤ 35

2x1 + x2 ≤ 60

x1, x2 ≥ 0

• The objective function Z represents the total profit made by producing x1 units of P1 and x2 units of P2.
• The production constraints limit the number of units that can be produced due to the limited facilities available for production. The labor constraint limits the number of units that can be produced due to the number of workers employed by the company.
• The non-negative variables constraint ensures that only positive values of x1 and x2 are considered. This LP problem can be solved using various methods, including graphical method or simplex method.

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