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Refer to Example 3. Suppose the demand for raw rubber increases by 40%, the demand for tires increases by 30%, and the demand for other rubber-based products decreases by 10%. Find the level of production for each subsidiary in order to meet this demand. (Round your answers to one decimal place.) raw rubber million tires $ million other rubber-based products $ $ million APPLIED EXAMPLE 3 An Input-Output Model for a Three-Product Company TKK Corporation, a large conglomerate, has three subsidiaries engaged in producing raw rubber, manufacturing tires, and manufacturing other rubber-based goods. The production of 1 unit of raw rubber requires the con- sumption of 0.08 unit of rubber, 0.04 unit of tires, and 0.02 unit of other rubber- based goods. To produce 1 unit of tires requires 0.6 unit of raw rubber, 0.02 unit of tires, and 0 unit of other rubber-based goods. To produce 1 unit of other rub- ber-based goods requires 0.3 unit of raw rubber, 0.01 unit of tires, and 0.06 unit of other rubber-based goods. Market research indicates that the demand for the following year will be $200 million for raw rubber, S800 million for tires, and $120 million for other rubber-based products. Find the level of production for each subsidiary in order to satisfy this demand. Solution View the corporation as an economy having three sectors and with an input-output matrix given by rubber Times Goods Raw rubber 0.08 0.60 0.30 A = Times 0.04 0.02 0.01 Goods 0.02 0 0.06 Using Equation (18), we find that the required level of production is given by X = (1 - A)-'D where x, y, and z denote the outputs of raw rubber, tires, and other rubber-based goods and where 200 D=800 120 Now, 0.92 -0.60 -0.307 I-A-0.04 0.98 -0.01 -0.02 0 0.94 You are asked to verify that 1.12 0.69 0.37 (1 - A)-! -0.05 1.05 0.03 L0.02 0.01 1.07 Therefore, 1.12 0.69 0.37 200 820.4 x = (1 - A) D = 0.05 1.05 0.03 800 8536 0.02 0.01 1.07 120 140.4 To fulfill the predicted demand, 5820 million worth of raw rubber. 5854 million worth of tires, and S140 million worth of other rubber-based goods should be produced