Goal Assignment Management Science

Alpha company produces two kinds of fancy products, pen holder and paper tray. Production of either a pen holder or a paper tray requires 1 hour of production capacity in the plant. The plant has a maximum production capacity of 12 hours per week. Because of the limited sales capacity, the maximum number of pen holders and paper trays that can be sold are 7 and 10 per week, respectively. The gross margin from the sale of a pen holder is Rs. 90, and Rs. 45 for a paper tray. The overtime hour should not exceed 3 hours/week.
The plant manager has set the following goals arranged in the order of importance.
(a) He wants to avoid any underutilization of production capacity.
(b) He wants to limit the overtime hours to 3 hours.
(c) He wants to sell as many pen holders and paper trays as possible. Since, the gross margin from the sale of a pen holder is set at twice the amount of profit from a paper tray, he has twice as much desire to achieve the sales goal for pen holders as for paper trays.
(d) He wants to minimize the overtime operation of the plant as much as possible. Formulate this as a goal programming problem

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