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 $25 to $26? From $41 to $42? From $65 to $667 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 $25 to $267 units at $25 per-unit : units at $26 per-unit = : (i) What happens to annual units demanded for the product if the firm increases the per-unit price from $41 to $42? units at $41 per-unit : units at $42 per-unit = : (iii) What happens to annual units demanded for the product if the firm increases the per-unit price from $65 to $667 units at $65 per-unit = : units at $66 per-unit = : (@ (d) (e) (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 and that annual demand by l:l units for every $1 in price increase. Show the mathematical model for the total revenue (TR) in terms of p, which is the annual demand multiplied by the unit price. TR = Based TR at $36 per-unit = TR at $48 per-unit on other considerations, the firm's management will only consider price alternatives of $36, $48, and $60. Use your medel from part (b) to determine the price alternative that will maximize the total revenue. [ TR at $60 per-unit = : Given the constraints, the Total Revenue is maximized at $ : per-unit. What are the expected annual demand and the total revenue corresponding to your recommended price? d = TR = L7 s ]