LT 2: I can develop cost and revenue functions and can explain their role in profit and break-even analysis, and I can use supply and demand functions and explain their role in market equilibrium analysis. The demand for your factory-made skateboards, in weekly sales, is \( q=-4 p+ \) 51 if the selling price is \( \$ p \). If you are selling them at that price, you can obtain \( q=2 p-33 \) skateboards per week from the factory. What will happen if the selling price is \( \$ 15 \) ? The breakeven point is \( \$ 15 \). There will be a surplus when the selling price is \( \$ 15 \). There will be a shortage when the selling price is \( \$ 15 \). The equilibrium price is \( \$ 15 \). There will be a profit when the selling price is \( \$ 15 \).

Let’s dive into the world of skateboards and how they dance in balance with supply and demand! When you set the selling price at $15, we plug that into the demand function: \( q = -4(15) + 51 = 3 \). This means customers want 3 skateboards weekly. On the flip side, using the supply function: \( q = 2(15) - 33 = -3 \), it indicates the factory can't produce any skateboards at that price! Technically, that’s a shortage since supply is negative—skateboards aren’t coming off the factory line, and customers are left hanging. Hopping into historical context, the relationship between supply and demand isn’t just a recent phenomenon; it dates back to Adam Smith in the 18th century! He introduced the idea of the "invisible hand," suggesting that self-interest in a free market leads to economic prosperity. This was revolutionary and laid the groundwork for modern economic principles, where prices fluctuate based on available goods and consumer desire. Who knew skateboards had historical roots, right?