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 $43 to $44? From $67 to $68? 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 $43 to $44? units at $43 per-unit = units at $44 per-unit = (III) What happens to annual units demanded for the product if the firm increases the per-unit price from $67 to $68? units at $67 per-unit = units at $68 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 --Select-- and that annual demand-Select--- v by units for every $1 in price increase. (iii) What happens to annual units demanded for the product if the firm increases the per-unit price from $67 to $68? units at $67 per-unit = units at $68 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 ---Select--- V and that annual demand ---Select--- v 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 $36, $48, and $60. Use your model from part (b) to determine the price alternative that will maximize the total revenue. TR at $36 per-unit = $ TR at $48 per-unit = $ TR at $60 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 =