18) A company manufactures two types of products X and Y on facilities, A, B, C, D, E, and F having production capacities as under. Facilities. Production capacity to produce 100 of X OR 150 of Y 80 of X OR 80 of Y 100 of X OR 200 of Y A B D 120 of X OR 90 of Y E 60 of X only (Testing facility for product X) F 60 of Y only. (Testing facility for product Y) If the profit contribution of product X is $ 40 per unit and that of Y is $ 30 per unit, find the optimal product mix for maximizing the profit by simplex algorithm.