Question

Indian Institute of Technology (IITs) delivers three courses: Mechanical Engineering, Electrical Engineering, and Computer Science. These products have the following resources requirements:

Course	Cost/Unit	Labour-Hours/Unit
Mechanical Engineering	$7.00	2
Electrical Engineering	$10.00	3
Computer Science	$35.00	5

IIT has a daily teaching budget of $5,000.00 and a maximum budget of 800 hours of labour. Selling prices are $15.00, $25.00 and $55.00 respectively. Maximum daily customer demand for Computer Science course is 100 units. The University desires to know the optimal product mix that will maximize profit. Formulate a linear programming model for this problem.

Answer 1

As the university wants to maximize the profit we will formulate a maximization problem which maximises the revenue.

Decision Variables:

Let x, y, z are the unit of couses in Mechanical Engg, Electrical Engg and computer science respectively in optimal product mix

Obj Function: Maximise 15*x+25*y+55*z (i.e. Total revenue by selling the courses)

Subject to:

cnstraint1: Daily teaching budget can be owritten as

7*x + 10*y + 35*z <= 5000

constraint2: daily labout hour constraint can be written as

2*x + 3*y + 5*z <= 800

constraint3: maximum demand of computer science course can be formulate as

z <= 100

Constraint4: Non negativity constraint

x > =0, y >= 0, z >= 0