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Let's first address part (a) of the problem, which asks for the price that should be charged for the units in stock.

The demand equation provided is:
\[
p = -0.16x + 224
\]
where:
- $p$ is the price,
- $x$ is the quantity sold (or in stock).

For part (a), we are given that there are 50 television sets in stock, so we substitute $x = 50$ into the equation to find the price $p$:

\[
p = -0.16(50) + 224
\]
Let's calculate that:

\[
p = -8 + 224 = 216
\]

So, the price that should be charged is **$216.00**.

Would you like more details or explanations on this step?

Here are a few related questions you might find helpful:
1. How can we calculate the revenue function from the demand equation?
2. How do we find the quantity $x$ that maximizes revenue?
3. What is the formula for calculating maximum revenue?
4. How do we find the vertex of a quadratic equation?
5. What other methods can we use to maximize profit using a demand equation?

**Tip**: Always remember that the revenue is maximized at the vertex of the quadratic function formed from the price and quantity.

The price p and the quantity x sold of a small flat-screen television set obeys the demand equation p = -0.16x + 224. How much should be charged for the television set if there are 50 television sets in stock?

Learn how to calculate the price of a flat-screen television using a linear demand equation. Given the equation p = -0.16x + 224, determine the price when 50 units are in stock.

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