A factory is in a position to manufacture three products P. Q and R. Raw material required for each unit of P, Q and R is 1kg, 2kg and 2.5kg respectively and costs N$2. Total raw material is 350kg. 

The products undergo processing on a machine having production hours of 160 hours in a day shift and 192 hours in a night shift. Times required per unit of production are as follows: Product Day shift Night shift P 2.0 2.5 Q 3.0 4.0 R 1.0 1.5 The machine costs N$ 1 per hour. Selling prices of P, Q and R are N$ 8, N$12 and N$3.5.

 There is a contract of 50 units of product P and a maximum of 150 units of R can be sold. 

REQUIRED:

Find the optimum solution to this problem using simplex method of linear programming.