6. A manufacturer produces three models (I, II, and III) of a certain product. He uses two types of raw materials (A and B) of which 400 ad 600 units respectively are available. The raw material requirements per unit of the three models are given below: Raw Requirement per unit of given mater models ial II III A 2 5 B 4 2 7 The labour time for each units of model-I is twice that of model-II and three times that of model-III. The entire labour force of the factory can produce the equivalent of 2500 units of model-I. A market survey indicates that minimum demand of the tree models are 500, 500, and 375 units. However, the ratio of the number of units produced must be equal to 3:2:5. Assume that profits per unit of model I, II, and III are Taka 60, 40, and 100 respectively. Formulate the problem as a linear programming model in order to determine the number of units of each product which will maximize profit. Maximize, Z = 60x1 + 40x, + 100x3 2x1 + 3x, + 5x;