$2-43$ Variable Cost to Break Even

General Mills makes Nature Valley granola bars, Cheerios cereal, Yoplait yogurt, H$$agen$-$Dazs ice cream, and many other food products. Suppose the product manager of a new General Mills cereal has determined that the appropriate wholesale price for a carton of the cereal is $$48.$ Fixed costs of the production and marketing of the cereal are $$19$ million.

The product manager estimates that she can sell $800,000$ cartons at the $$48$ price. What is the largest variable cost per carton that General Mills can pay and still achieve a profit of $$1$ million?

Suppose the variable cost is $$25$ per carton. What profit $($or loss$)$ would General Mills expect?