A company produces two types of product: A and B. To manufacture, product A requires 5 parts of type I and 3 parts of type II; B requires 4 parts of type I and 2 parts of type II. The profit is 20 for A and 30 for B. The company aims to achieve a weekly profit of 2000. The production time per unit of A is 7 man-hours and per unit of B is 3 man-hours. The company employs seven people in the production department and would like to keep within the 250 available hours of work each week. A contract has been signed with a supplier to deliver up to 80 parts of type I and 60 parts of type II. It is possible to order more parts but they would be much more expensive. The manufacturing capacity of the machine for both products combined is limited to a maximum of 80 products per week. The company has a strategic target to produce at least 50 units of each product per week.

a )Formulate the problem as a goal programming problem.

b) If weekly working hours goal is 5 times important than the other goals formulate the problem as a weighting goal programming problem.