1. **State the problem:** Anon runs a snowboard business charging 12 per snowboard with 36 rentals per day. For each 0.50 decrease in price, rentals increase by 2. We want to find the price that maximizes revenue. 2. **Define variables:** Let $x$ be the number of 0.50 decreases in price. 3. **Express price and quantity as functions of $x$:** Price per snowboard: $$p = 12 - 0.5x$$ Number of rentals: $$q = 36 + 2x$$ 4. **Write the revenue function:** Revenue $$R = p \times q = (12 - 0.5x)(36 + 2x)$$ 5. **Expand the revenue function:** $$R = 12 \times 36 + 12 \times 2x - 0.5x \times 36 - 0.5x \times 2x$$ $$R = 432 + 24x - 18x - x^2$$ $$R = 432 + 6x - x^2$$ 6. **Rewrite revenue function:** $$R(x) = -x^2 + 6x + 432$$ 7. **Find the vertex of the parabola to maximize revenue:** The vertex $x$-value is given by $$x = -\frac{b}{2a} = -\frac{6}{2 \times (-1)} = 3$$ 8. **Calculate the price at $x=3$:** $$p = 12 - 0.5 \times 3 = 12 - 1.5 = 10.5$$ **Final answer:** The price that maximizes revenue is **10.5** per snowboard.