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

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.

  1. How many units can the firm sell at the $20 per-unit price? Round your answer to the nearest whole number.
  2. d =  units
  3. At the $70 per-unit price? Round your answer to the nearest whole number.
  4. d =  units
  5. What happens to annual units demanded for the product if the fim increases the per unit price from $26 to $27?
  6. If the firm increases the per unit price from $26 to $27, the number of units the firm can sell 
  7.  by .
  8. From $42 to $43?
  9. If the firm increases the per unit price from $42 to $43, the number of units the firm can sell 
  10.  by .
  11. What is the suggested relationship between the per-unit price and annual demand for the product in units?
  12. This suggests that the relationship between the per-unit price and annual demand for the product in units is 
  13.  between $20 and $70 and that annual demand for the product 
  14.  by  units when the price is increased by $1.
  15. 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.
  16. TR = 
  17. (800−10P)P
  18. 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.
  19. Total revenue is maximized at the $ 
  20.  price.
  21. What are the expected annual demand and the total revenue corresponding to your recommended price?
  22. Round your answer to the nearest whole number.
  23. d =  units
  24. Round your answer to the nearest dollar.
  25. TR = $  

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