A manufacturing company is considering whether to establish a new distribution center $($DC$)$ in a particular region. The initial investment for setting up the new DC is Rs$.10,00,000.$ If the new DC is successful, it is expected to generate annual savings of Rs$.3,00,000$ due to reduced transportation costs and improved efficiency. However, there's uncertainty about market demand in that region, with a $70\%$ chance of high demand and a $30\%$ chance of low demand. What would be the expected annual savings in case of successful setting up of new DC with $0\mathrm{.}2$ discount rate?$$

$2,75,000$

$1,75,000$

$75,000$

None of the above