A company has a maximum of 14 hours of labor to produce 2 pr

A company has a maximum of 14 hours of labor to produce 2 products daily. A unit of product 1 requires 4 hours while a unit of product 2 requires 3. For producing, it\'s necesary a raw material of which 12 units are available daily, requiring 2 units to produce a unit of product 1 and 3 units to produce a unit of product 2. Assume you want to maximize profit.

Raises a linear programming model.

Solve by simplex method.

Step by step solution please.

Solution

Labour hours available <=14

Product I II

No of units x y

Lab hours 4 3

Raw mat 2 3

Raw mat available = 12

Writing constraints in terms of x and y

4x+3y<=14

and 2x+3y<=12

Subtracting we get 2x<=2 or x <=1

Hence x can be 0 or 1

y can be <=4

Our objective is to maximise profit

Or minimise cost

Cost C= 14l+12 m where l = labour charge per hour and m = material cost per unit

Feasible solutions are (0,4) (1,3)

Since sales value is not given we cannot proceed further.