Calculate the actual cost, revenue and profit to produce and sell the 10 th ounce of the commodity. Then use the marginal functions approximate the cost, venue and profit to produce and sell the 10 th unit. Compare the results by filling in the blanks. sing the marginal cost function, the approximate cost to produce the 10 th ounce is roducing the 10 th ounce of the commodity actually costs sing the marginal revenue function, the approximate revenue from the sale of the 10 th ounce is he actual revenue from the sale of the 10 th ounce of the commodity is Jsing the marginal profit function, the approximate profit from the production and sale of the 10 th unit is The actual profit from the production and sale of the 10 th ounce of the commodity is high.

To calculate the actual cost, revenue, and profit for producing and selling the 10th ounce of a commodity, we need specific functions for cost, revenue, and profit. However, since you haven't provided those functions, I will outline the general approach to solve this problem. ### Step 1: Define the Functions Assume we have the following functions: - **Cost Function**: \( C(x) \) - the total cost to produce \( x \) ounces. - **Revenue Function**: \( R(x) \) - the total revenue from selling \( x \) ounces. - **Profit Function**: \( P(x) = R(x) - C(x) \) - the profit from selling \( x \) ounces. ### Step 2: Calculate Actual Values 1. **Actual Cost to Produce the 10th Ounce**: \[ C(10) - C(9) \] This gives the actual cost of producing the 10th ounce. 2. **Actual Revenue from the Sale of the 10th Ounce**: \[ R(10) - R(9) \] This gives the actual revenue from selling the 10th ounce. 3. **Actual Profit from the Production and Sale of the 10th Ounce**: \[ P(10) = R(10) - C(10) \] ### Step 3: Use Marginal Functions 1. **Marginal Cost**: \( C'(x) \) - the derivative of the cost function. - Approximate cost to produce the 10th ounce: \[ C(9) + C'(9) \] 2. **Marginal Revenue**: \( R'(x) \) - the derivative of the revenue function. - Approximate revenue from the sale of the 10th ounce: \[ R(9) + R'(9) \] 3. **Marginal Profit**: \( P'(x) = R'(x) - C'(x) \). - Approximate profit from the production and sale of the 10th ounce: \[ P(9) + P'(9) \] ### Step 4: Fill in the Blanks Now, you can fill in the blanks based on the calculations: - Using the marginal cost function, the approximate cost to produce the 10th ounce is **(insert value)**. - Producing the 10th ounce of the commodity actually costs **(insert value)**. - Using the marginal revenue function, the approximate revenue from the sale of the 10th ounce is **(insert value)**. - The actual revenue from the sale of the 10th ounce of the commodity is **(insert value)**. - Using the marginal profit function, the approximate profit from the production and sale of the 10th unit is **(insert value)**. - The actual profit from the production and sale of the 10th ounce of the commodity is **(insert value)**. ### Conclusion To complete this exercise, you will need the specific cost, revenue, and profit functions or their values at the relevant points (9 and 10 ounces). If you provide those, I can help you calculate the actual and approximate values.