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A memory chip is being designed to hold a number of transistors and heat sinks. The transistors hold memory while the heat sinks cool the chip. There must be at least one heat sink for every $2,000$ transistors to prevent overheating. Also, each transistor has an area of $2.0 \times 10^{-10}\text{mm}^{2}$ (square millimeters), each heat sink has an area of $3.6 \times 10^{-6}\text{mm}^{2}$, and the total area of transistors and heat sinks must be at most $2\text{mm}^{2}$. What is the approximate maximum number of transistors that the chip can hold according to this design?$\newline$ Choose $1$ answer:$\newline$ (A) $2.78 \times 10^{2}$$\newline$ (B) $5.56 \times 10^{5}$$\newline$ (C) $1.0 \times 10^{9}$$\newline$ (D) $1.0 \times 10^{10}$