For most products, higher prices result in a decreased demand, whereas lower prices result in an Increased demand. Let 0' = annual demand for a prpduct in units p = price per unit Assume that a firm accepts the rciidwing pricedemand relationship as being realistic: d : 1,000 12p where p must he between 320 and 560. (a) How many units can the firm seii at the $20 perennit price? At the $30 perrunit price? units at $20 persunit : : units at $30 pereunit : S (b) What happens to annual units demanded for the product if the firm increases the Def'Llfilt price from $25 to 526? From $44 to $45? From $65 to $66? What is the suggested relationship between the persunit price and annual demand for the product in units? (i) what happens to annuai units demanded for the produ(t it the rm increases the per-unit price from $25 to $26? units at 525 peFLmlt : : units at 525 per-unit : E (ii) What happens to annual units demanded for the produtt if the firm increases the permit price from $44 to $45? units at 544 perruhit = : units at 545 peFLmlt : : (iii) What happens to annual units demanded for the prpduct if the firm increases the perrunil price frpm $65 to $66? units at 565 perrunit : : units at sea per-unit : E (iv) what is the suggested relationship between the perrunil price and annuai demand for the product in units? This suggests that the relationship is and that annual demand by E units for every 51 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 $34, $46, and $58. Use your model from part (b) to determine the price alternative that will maximize the total revenue. TR at$34 perrunit = $\\:| TR at$46 per-unit : $\\:| TR at$Sa perrunit = 9: Given the constraints, the Total Revenue is maximized at 3; :I perfunit. (e) What are the expected annual demand and the total revenue corresponding to your recommended price? a\