This paper presents the production planning problem in industry with different operational constraints, including strategic aim of the company, profit goal, limit on finishing and furnace hours needed, cups manufactured with target values being imprecise in nature. The fuzzy goal programming techniques is applied to maximize the production capacity, maximize the profit, minimize the extra finishing labor and furnace hours, and ensure the manufacturing capacity. The objective of this paper is to elaborate a plan which takes manager's preferences into account. The results illustrate the flexibility of the proposed model by adjusting goal priorities with respect to importance of each objective and the aspiration level with respect to desired target values. LINDO 14.0 optimizer solver is used to draw results of the problem.