1. A manufacturer produces three models (I, II, and III) of a certain product. He uses two types of raw material (A and B) of which 4000 and 6000 units are available, respectively. The raw material requirements per unit of three models are given below. Raw Material A B I 3 2 Requirements per unit of given models II 4 9 III 7 5 The labor time for each unit of Model I is twice that of Model II and three times that of Model III. The entire labor force of the factory can produce the equivalent of 600 units of Model I. A market survey indicates that the minimum demand of the three models is 200, 200 and 150 units, respectively. However, the ratios of the number of units produced must be equal to 2:5:3. Assume that the profit per unit of Models I, II, and III are 30, 20, and 50 dollars. Formulate the problem as a linear programming model in order to determine the number of units of each product which will maximize profit.