Problem: As a fundraiser, Student Council sells pizza at the Spring Fling! They know from the past that they can sell 20 slices of pizza at $\$ 2.00$ a slice. If they lower the price by $\$ 0.25$, they can sell 5 more slices of pizza. At what price should they sell the pizza to maximize their revenue?
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Answer
\(\boxed{1.50}\) is the price per slice that maximizes the revenue.
Step 1 ：Let the price per slice be x and the number of slices sold be y. We know that if x = 2, y = 20, and if x = 2 - 0.25, y = 20 + 5.
Step 2 ：Using these two points, we can find the equation of the line relating x and y: y = 60 - 20x.
Step 3 ：To maximize the revenue, we need to find the value of x that maximizes the product of x and y (R = xy).
Step 4 ：R = x(60 - 20x).
Step 5 ：Taking the derivative of R with respect to x, we get: R' = 60 - 40x.
Step 6 ：Setting R' equal to 0, we find the critical point: x = 1.5.
Step 7 ：\(\boxed{1.50}\) is the price per slice that maximizes the revenue.
