Deanna runs a bakery that sells gourmet doughnuts. At $5 per doughnut she sells 100 doughnuts in a day. Her daily costs to make the doughnuts are $175. Deanna estimates that for each $0.50 decrease in cost she will sell
35 more doughnuts each day. The daily profits for the doughnuts can be modeled with the equation:
P(x) = (100+35x)(5 -0.5x) -175, where x represents the number of $0.50 decreases in price. Use
technology to graph the profit equation and determine the price per doughnut that Deanna should charge to
maximize her profits.

$3.21

Step-by-step explanation:

This question asks for use of technology, so you can use a hand graphing calculator or the desmos website (which I used).

I have attached the screenshot of this graph. We want the maximum value on the y axis (the axis representing profit). We can see that the highest point is at (3.571, 548.214), so this is when she makes the most money.

This means that she makes the most profit at 3.571 50 cent decreases.

3.571×0.5 is a decrease by $1.7855.

This means the best price is 5-1.7855, which is 3.2145. This can be rounded to $3.21