Task 2 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 (PL1 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. Determine the general formulas of the production rates 2. Determine a general formula for the number of different products per line. 3. Construct a sequence of the sum of the production rates per line (S1, S2...S9). Is there any relation between these sums? 4. Determine the maximum number of different products that can be produced at this factory. 5. 6. 7. 8. Determine the maximum possible production rate for any of the products and the minimum one. Calculate the range of production rates for the ninth production line. If the company would like to have a production rate approximately 5000. Does the available production lines support this. Calculate to the nearest integer how many days it is needed to run the nine production lines to produce 20000 transducer of product number 5. If the manager asked you which production line should be considered to produce product number 4 at a rate of approximately 2750 transducer/day. What will be your answer and why? Calculate how many production rates are available and what is needed to double this number. 9. 10. Task 2 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 (PL1 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. Determine the general formulas of the production rates 2. Determine a general formula for the number of different products per line. 3. Construct a sequence of the sum of the production rates per line (S1, S2...S9). Is there any relation between these sums? 4. Determine the maximum number of different products that can be produced at this factory. 5. 6. 7. 8. Determine the maximum possible production rate for any of the products and the minimum one. Calculate the range of production rates for the ninth production line. If the company would like to have a production rate approximately 5000. Does the available production lines support this. Calculate to the nearest integer how many days it is needed to run the nine production lines to produce 20000 transducer of product number 5. If the manager asked you which production line should be considered to produce product number 4 at a rate of approximately 2750 transducer/day. What will be your answer and why? Calculate how many production rates are available and what is needed to double this number. 9. 10
