3. Because of the poor air quality in Dallas (partly due to too many private cars in the traffic), DART wants to start up 4 new routes: between Plano and Dallas, between Richardson and Addison, between Plano and Richardson, and between Richardson and Dallas. Plano and Dallas municipalities put down $800,000 and $200,000, respectively, to finance these routes. DART is facing the question of investing a total of $1,000,000 (=800,000+200,000) to four routes such that at least 80% of the investment is made for the routes involving Plano and at least 30% of the investment is made for the routes involving Dallas. Richardson - Addison and Plano - Richardson routes are almost of equal length and DART can make a profit at the rate of 20% per year for each dollar invested. These rates are 0% for the Plano - Dallas route and 10% for the Richardson - Dallas route.
a) Give an LP formulation that maximizes DART's return on investment in a year.
b) Argue that there can be an optimal solution without investing into Richardson - Addison route.
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