Pearson Manufacturing wants to maximize profit from the sale of 2 products. Widgets produce a profit of $35 per unit and Things produce a profit of $45 per unit. Demand requires the total number of units produced per day not to exceed 3000 units and that the number of Things produced be greater than or equal to half of the number of Widgets produced. To meet demand, Pearson must produce at least 500 Widgets per day. How many of each should be produced to maximize profit and what will the maximum profit be?