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The problem provides the consumer demand equation for tissues:

\[
x = (96 - p)^2
\]

where $ p $ is the price per case of tissues (in dollars), and $ x $ is the demand in weekly sales. We are tasked with determining the price elasticity of demand $ E $ when the price is set at $ p = 29 $. 

### Step-by-step solution:

1. **Price Elasticity Formula:**

The formula for price elasticity of demand $ E $ is:

\[
E = \frac{p}{x} \cdot \frac{dx}{dp}
\]

2. **Differentiate the demand equation:**

Given that $ x = (96 - p)^2 $, we differentiate $ x $ with respect to $ p $:

\[
\frac{dx}{dp} = 2(96 - p)(-1) = -2(96 - p)
\]

3. **Substitute values into the formula:**

We need to evaluate the price elasticity at $ p = 29 $.

- First, calculate $ x $ when $ p = 29 $:
  
\[
x = (96 - 29)^2 = 67^2 = 4489
\]

- Next, calculate $ \frac{dx}{dp} $ when $ p = 29 $:

\[
\frac{dx}{dp} = -2(96 - 29) = -2(67) = -134
\]

4. **Substitute these values into the price elasticity formula:**

\[
E = \frac{29}{4489} \cdot (-134)
\]

Now we compute the result:

\[
E = \frac{29 \times (-134)}{4489} = \frac{-3886}{4489} \approx -0.866
\]

### Interpretation:
Since the price elasticity $ E = -0.866 $, the demand is inelastic at this price level. The negative sign indicates that an increase in price will result in a decrease in demand, and specifically, the demand is decreasing by about 0.866% for each 1% increase in price.

Would you like any further clarification or details? Here are some related questions:

1. What does it mean when demand is inelastic?
2. How would the elasticity change if the price were higher?
3. Can elasticity be positive, and under what circumstances?
4. How does elasticity help in setting prices in real-world markets?
5. What would happen to the elasticity if the demand equation were different?

**Tip:** Price elasticity of demand helps businesses understand how sensitive consumers are to changes in price, guiding decisions in pricing strategies.

The consumer demand equation for tissues is given by x = (96 - p)^2, where p is the price per case of tissues (in dollars) and x is the demand in weekly sales. Determine the price elasticity of demand when the price is set at $29.

Learn how to calculate the price elasticity of demand using the demand equation x = (96 - p)^2. This detailed solution shows step-by-step calculations for finding the elasticity at a price point of $29, involving differentiation and elasticity interpretation.

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