27. A production manager faces the problem of job allocation between two assembly lines. The production rate of assembly line 1 is 10 units per hour, and the production rate of assembly line 2 is 12 units per hour. The normal working period for both lines is 8 hours per day. The production manager has set the following goals for the next day, listed in order of their importance:

(i) Avoid any underachievement of the production level, which is set at 200 units of product.

(ii) Avoid any overtime operation of line 2 beyond 4 hours.

(iii) Avoid any underutilisation of regular working hours (assign differential weights according to the relative productivity of the two lines).

(iv) Minimise overtime in both assembly lines.

Formulate a goal programming model and solve it.