(16 points] Products X and Y are purchased wholesale from a single supplier and then sold in two cities, A and B. The same number of product X is sold in cities A and B, and the same number of product Y is sold in cities A and B. The supplier charges $8 per unit of X and $6 per unit of Y. Assume that all products bought from the supplier are actually sold, and that it is possible that none of a particular product is bought from the supplier or sold. There are three additional sales constraints: (i) In city A, each unit of X sells for $30, each unit of Y sells $10, and there must be a total sales amount of at least $600. (ii) In city B, each unit of X sells for $10, each unit of Y sells $20, and there must be a total sales amount of at least $500. (iii) The sum total number of products X and Y sold in city A must be at least 40. Calculate how many units of X and Y should be sold in each city so that the total wholesale purchase cost to cover both cities is minimized and all conditions and constraints above are satisfied (You may assume there is a minimum total purchase cost to cover both cities). To earn full points, your solution must include a neat, labeled diagram of the feasible region and all calculations/justifications