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 = 1,000 12p

where p must be between $20 and $80.

(a) How many units can the firm sell at the $20 per-unit price? At the $80 per-unit price?

units at $20 per-unit=

units at $80 per-unit=

(b) What happens to annual units demanded for the product if the firm increases the per-unit price from $27 to $28? From $44 to $45? From $65 to $66? What is the suggested relationship between the per-unit price and annual demand for the product in units?

(i) What happens to annual units demanded for the product if the firm increases the per-unit price from $27 to $28?

units at $27 per-unit=

units at $28 per-unit=

(ii)What happens to annual units demanded for the product if the firm increases the per-unit price from $44 to $45?

units at $44 per-unit=

units at $45 per-unit=

(iii)What happens to annual units demanded for the product if the firm increases the per-unit price from $65 to $66?

units at $65 per-unit=

units at $66 per-unit=

(iv) What is the suggested relationship between the per-unit price and annual demand for the product in units? This suggests that the relationship is linear or nonlinear and that annual demand rises or falls by _______ units for every $1 in price increase.

(c) Show the mathematical model for the total revenue (TR) in terms of p, which is the annual demand multiplied by the unit price.

TR =

(d) Based on other considerations, the firm's management will only consider price alternatives of $32, $44, and $56. Use your model from part (b) to determine the price alternative that will maximize the total revenue.

TR at $32 per-unit=$

TR at $44 per-unit=$

TR at $56 per-unit=$

Given the constraints, the Total Revenue is maximized at $________ per-unit.

(e) What are the expected annual demand and the total revenue corresponding to your recommended price?

d=TR=$