Liza needs to make at least 6,286 donuts for the average cost per donut to be less than her selling price of $2.00 per donut. So, the correct option is A.
The student's question revolves around calculating the number of donuts, x, that Liza will have to make to ensure that her average cost per donut, D(x), is less than her selling price of $2.00. To find this, we need to set up an inequality where the average cost per donut is less than the selling price:
D(x) = 11,000 + 0.25x
To determine the number of donuts (x) needed to make D(x) less than $2.00, the following inequality must be true:
D(x)/x < $2.00
By substituting the D(x) expression, we get:
(11,000 + 0.25x) / x < $2.00
Solving the inequality, we find:
11,000 + 0.25x < 2x
11,000 < 2x - 0.25x
11,000 < 1.75x
x > 11,000 / 1.75
By solving this, we find that x > 6,285.71.
Since Liza cannot make a fraction of a donut, she will need to make at least 6,286 donuts for her average cost to be less than her selling price per donut.