BP Cola must decide how much money to allocate for new soda and traditional soda advertising over the coming year. The advertising budget is $$12,000,000.$ Because BP wants to push its new soda at least one$-$half of the advertising budget is to be devoted to new soda advertising. However, at least $$2,000,000$ is to be spent on its traditional sodas. BP estimates that each dollar spent on traditional sodas will translate into $100$ cans sold, whereas, because of the harder sell needed for new products, each dollar spent on new sodas will translate into $50$ cans sold.

To attract new customers, BP has lowered its profit margin on new sodas to $2$ cents per can as compared to $4$ cents per can for traditional sodas. How should BP allocate its advertising budget if it wants to maximize its profits while selling at least $750$ million cans? $($Let $x_1=$ be the amount spent on advertising for the new soda. Let $x_2=$ be the amount spent on advertising for the traditional soda.$)$

$(x_1,x_2)=()$