A chemical plant makes three major products on a weekly basis. Each of these products requires a certain quantity of raw chemical and different production times, and yields different profits. The pertinent information is in Table P16.4. Note that there is sufficient warehouse space at the plant to store a total of 450 kg/week.

(a) Set up a linear programming problem to maximize profit.

(b) Solve the linear programming problem with the simplex method.

(c) Solve the problem with a software package.

(d) Evaluate which of the following options will raise profits the most: increasing raw chemical, production time orstorage.

Table P16.4 Resource Availability Product 2 Product 3 Praduct 1 2500 kg 55 hr/week 12 kg/kg 0.2 hr/kg 6 kg/kg 4 kg/kg 0.1 /kg $30/kg Raw chemical Produclion lime 0.05 he/kg Proht $35/kg $30/kg