Can someone me with this calculus? ! don't forget to show your work : )

  $12.50

Step-by-step explanation:

Since the cost is $5, at a selling price of x, the profit on each pair is (x -5). The profit for the day is the profit on each pair multiplied by the number sold:

  profit = (x -5)·100(20 -x)

This is the expression for a quadratic function that has zeros at  x=5 and x=20 and that opens downward (the leading coefficient is -100). The vertex (maximum) is found on the axis of symmetry, halfway between the zeros. The value of x there is ...

  (5 + 20)/2 = 12.5

The manufacturer should sell the sunglasses at $12.50 apiece to maximize profit.