The production manager of a company wants to schedule a week's production run for two products P1 and P2, each of which requires the labour and materials as shown below:

The weekly availability of resources is limited to 600 labour hours, 1000 kg of material M1 and 1,200 kg of M2. The unit profit for P1 and P2 is Rs 20 and Rs 32, respectively.
Products P1 and P2 are, in fact, new models and are replacements of the older ones which have been discontinued very recently. The manager would like to maximise profit but he is equally concerned with maintaining workforce of the division at nearly constant level in the interest of employee morale. The workforce, which consists of people engaged in production, sales, distribution, peons and other general staff, consisted of 108 persons in all. From a detailed study, it is known that production of one unit of P1 would maintain 0.3 person in the workforce, while one unit of P2 would maintain 0.75 person.
Had the production manager been considering only maximising profit, without regard to maintaining the workforce, he would do so by producing 167.67 units of P1 and 66.67 units of P2 (this can be checked by solving the problem as an LPP). On the basis of the available capacity, this would yield a profit equal to 167.67 x 20 + 66.67 x 32 or Rs 5,486.67. However, this would maintain 100.3 people in the workforce. The manager feels that probably he could increase the workforce requirement to desired level by accepting somewhat lower profit. In keeping with this, the following two goals are established: a profit of Rs 5,400 per work and a workforce of 108 persons. Formulate and solve this as a goal programming problem

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Labour Hours Material M (kg) Material M (kg) P 2 Product 4 5 P2 454