BP Cola must decide how much money to allocate for new soda and traditional soda advertising over the coming year. The advertising budget is $10,000,000. Because BP wants to push its new sodas, 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. Let X ₁ = amount invested in new soda advertising ; and X ₂ = amount invested in traditional soda advertising.

The constraint that would ensure the number of new cans sold is at least 10 million more than the number of traditional sold is: