1.A firm has a total revenue function based on producing two goods represented by the following equation.

The firm also has a variable cost of . Regardless of how much the firm produces, they have a cost of 800.

The firm also has machinery so that only 30 total units of either good can be produced in a given time period.

Using calculus, what is the quantity of each good that should be produced to maximize profits? Verify using calculus that it is indeed a maximum. (15 points)