The development department is willing to develop an algorithm to its production lines. The company has 9 different production lines that wish to control its production rate based on customer needs. Production line number 1 can produce 7 different products (PL1 can produce 1 to 7) different transducers that can produce per day 150 (transducer/day) to 1050 (transducer/day). Production line 2 has 9 (PLi can produce 1 to 9) different transducers that can produce per day 170 (transducer/day) to 1530 (transducer/day). The initial production rate follow an arithmetic progression such that PL1( product 1) = 150, PL2(product 1) =170, and so on. The production rates within the same production line follow an arithmetic progression sequence. However, the number of different products per line increases using geometric progression (N of different products per line = 7, 9, ....) 1. 2. 3. Determine the general formulas of the production rates Determine a general formula for the number of different products per line. Construct a sequence of the sum of the production rates per line (S1, S2, ..S9). Is there any relation between these sums? Determine the maximum number of different products that can be produced at this factory. 4