Question

Smaran being a manufacturer produces nuts and bolts for industrial machinery. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts while it takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs 2.50 per package on nuts and 1 per package on bolts. Form a linear programming problem to maximize his profit, if he operates each machine for at most 12 hours a day.

Answer 1

	Nuts	Bolts	Maximum
Machinery A	1	3	12
Machinery B	3	1	12
Profit	2.50	1

Let the number of units of nuts x & bolts be y it takes 1 hour on machine A for a nut and 3 hours on machine 13 for a nut maximum time available for machine A is 12 hours. 

∴ x + 3y ≤ 12 

3x + y ≤ 12 

Negative units cannot be produced: x, y ≥ 0 our objective is to maximum profit the LPP is Maximize 

= 2.5 x + y subject to 

x + 3y ≤ 12 

3x + y ≤ 12 

and x ≥ 0, y ≥ 0