For most products, higher prices result in a decreased demand, whereas lower prices result in an increased demand. Let

d = annual demand for a product in units

p = price per unit

Assume that a firm accepts the following price-demand relationship as being realistic:

d = 800 – 10p

where p must be between $20 and $70.

- How many units can the firm sell at the $20 per-unit price? Round your answer to the nearest whole number.
- d = units
- At the $70 per-unit price? Round your answer to the nearest whole number.
- d = units
- What happens to annual units demanded for the product if the fim increases the per unit price from $26 to $27?
- If the firm increases the per unit price from $26 to $27, the number of units the firm can sell
- by .
- From $42 to $43?
- If the firm increases the per unit price from $42 to $43, the number of units the firm can sell
- by .
- What is the suggested relationship between the per-unit price and annual demand for the product in units?
- This suggests that the relationship between the per-unit price and annual demand for the product in units is
- between $20 and $70 and that annual demand for the product
- by units when the price is increased by $1.
- Show the mathematical model for the total revenue (TR), which is the annual demand multiplied by the unit price. Express your answer in terms of p.
- TR =
- (800−10P)P
- Based on other considerations, the firm’s management will only consider price alternatives of $30, $40, and $50. Use your model from part (c) to determine the price alternative that will maximize the total revenue.
- Total revenue is maximized at the $
- price.
- What are the expected annual demand and the total revenue corresponding to your recommended price?
- Round your answer to the nearest whole number.
- d = units
- Round your answer to the nearest dollar.
- TR = $