Janette Douglas is coordinating a bake sale for a nonprofit organization. The organization has acquired $2,200 in donations to hold the sale. The table below shows the amounts and costs of ingredients used per batch of each baked good:
One batch results in 10 brownies, 12 cupcakes, 8 peanut butter cups, and 12 shortbread cookies. Each batch of brownies can be sold for $6.00, cupcakes for $10.00, peanut butter cups for $12.00, and shortbread cookies for $7.50. The organization anticipates that a total of at least 4,000 baked goods must be made. For adequate variety, at least 30 batches of each baked good are required, except for the popular brownies, which require at least 100 batches. In addition, no more than 40 batches of shortbread cookies should be made. How can the organization best use its budget and make the largest amount of money?