A linear revenue function is \( R=38.67 x \). (a) What is the slope \( m \) ? (b) What is the marginal revenue \( \overline{M R} \) ? What does the marginal revenue mean? If the number of units sold is increased by this amount, the revenue increase Each additional unit sold decreases the revenue by this many dollars. (c) What is the revenue received from selling one more item if 43 are currently beir \( \$ \square \) inits sold yields this many dollars in revenue. What is the revenue received from selling one more item if 82 are being sold? \( \$ \square \)

To analyze the linear revenue function \( R = 38.67x \), where \( R \) is the revenue and \( x \) is the number of units sold, we can answer the questions as follows: ### (a) What is the slope \( m \)? The slope \( m \) of the linear function \( R = 38.67x \) is the coefficient of \( x \). Therefore, the slope \( m \) is: \[ m = 38.67 \] ### (b) What is the marginal revenue \( \overline{M R} \)? The marginal revenue \( \overline{M R} \) is the change in revenue resulting from selling one additional unit. In a linear revenue function, the marginal revenue is equal to the slope of the revenue function. Thus: \[ \overline{M R} = 38.67 \] **What does the marginal revenue mean?** Marginal revenue represents the additional revenue generated from selling one more unit of a product. In this case, if the number of units sold is increased by one, the revenue will increase by \( \$38.67 \). ### (c) What is the revenue received from selling one more item if 43 are currently being sold? To find the revenue received from selling one more item when 43 units are sold, we can calculate the revenue for 43 units and then for 44 units: 1. Revenue for 43 units: \[ R(43) = 38.67 \times 43 = 1652.81 \] 2. Revenue for 44 units: \[ R(44) = 38.67 \times 44 = 1691.48 \] 3. The revenue received from selling one more item (from 43 to 44 units): \[ R(44) - R(43) = 1691.48 - 1652.81 = 38.67 \] Thus, the revenue received from selling one more item if 43 are currently being sold is: \[ \$38.67 \] ### What is the revenue received from selling one more item if 82 are being sold? Similarly, we can calculate the revenue for 82 units and then for 83 units: 1. Revenue for 82 units: \[ R(82) = 38.67 \times 82 = 3160.94 \] 2. Revenue for 83 units: \[ R(83) = 38.67 \times 83 = 3199.61 \] 3. The revenue received from selling one more item (from 82 to 83 units): \[ R(83) - R(82) = 3199.61 - 3160.94 = 38.67 \] Thus, the revenue received from selling one more item if 82 are currently being sold is: \[ \$38.67 \] ### Summary of Answers: - (a) Slope \( m = 38.67 \) - (b) Marginal revenue \( \overline{M R} = 38.67 \) - (c) Revenue from selling one more item if 43 are sold: \( \$38.67 \) - Revenue from selling one more item if 82 are sold: \( \$38.67 \)