There are two types of residents in a city: $70\%$ low$-$income residents and $30\%$ high$-$

income residents. The government is considering two projects with same costs. If project

A is taken, each low$-$income resident can save his transportation cost by $$1,000$ and each

high$-$income resident can save his transportation cost by $$750.$ If project B is taken, each

low$-$income resident can save his transportation cost by $$800$ and each high$-$income

resident can save his transportation cost by $$1,350.$

If money is more important to low$-$income people than to high$-$income people, which

project is better?

Let the weights assigned to benefits and costs of low$-$income and high$-$income residents be $w$ and $1,$

respectively. What values of $w$ make project A better?