3. [5 points] We are asked to design an embedded system that will be responsible

Question

3. [5 points] We are asked to design an embedded system that will be responsible for executing five computational tasks, denoted by Ti, T2, T3, T4, Ts. Our choices are as follows: $100 CPU core that can handle tasks Ti, T2, T3; $200 GPU core that handle tasks T4, T5; $200 FPGA core that can handle tasks T?, T3, Ts; $70 ASIC core that can handle task T4; $60 ASIC core that can handle task Ti; $50 ASIC core that can handle task T2; Given the above choices, we need to select a minimum-cost collection of cores such that all tasks are handled. Formulate this question as a set covering problem

Explanation / Answer

So, in thi sproblem we have set of 5 tasks {T1, T2, T3, T4, T5} that needs to be executed via an embedded system.

Now we need to choose such configurations from the list of available choice so that the cost of the cores is miminal and we are able to run these 5 tasks as well. So lets see various options that we can have:-

OPTION1:- $100 CPU CORE (T1, T2, T3) + 200$ GPU (T4, T5) = 300$ (T1, T2, T3, T4, T5) [best coice]

OPTION 2:- 200$ FPGA CORE (T1, T3, T5) + 70$ (T4) + 50$ (T2) = 200 + 120 = 320$  (T1, T2, T3, T4, T5)

OPTION 3:- 60 (T1) + 50 (T2) + 200$ (T1, T3, T5) + 70 (T4) = 380$ (T1, T2, T3, T4, T5)

OPTION4:- 200$ (T1, T3, T5) + 200$ (T4, T5) + 70 (T4) = 470$ (T1, T2, T3, T4, T5)

Thus Option1 gives us the minimal cost of collection of cores such that all the tasks are handled. [ANS]

Please let me know in case of any clarifications required. Thanks!

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