Question

1. A firm manufactures two products; the net profit on product 1 is Rupees 3 per unit and Rupees 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. (solve with graphical method)

Answer 1

$3\cdot x_1+5\cdot x_2\rarr max$

$x_1+2\cdot x_2\le800;\\ 3\cdot x_1+2\cdot x_2\le1200;\\$

$x_1\ge0,x_2\ge0$

Extreme Point Coordinates:

$(400,0)$ : $z=1200$

$(200,300)$ : $z=2100$

$(0,400)$ : $z=2000$

optimal solution:

 x₁=200,x₂=300 and max Z=2100.