For most products, higher prices result in a decreased demandr whereas lower prices result in an increased demand. Let 0' = annual demand fora product in units ,0 = price per unit Assume that a rm accepts the following pricedemand relationship as being realistic: d = 1,ooo 12p where p must be between $20 and $80. (a) Hole.I many units can the rm sell at the $20 per-unit price? At the $80 per-unit price? units at $20 perunit = |:|x units at $80 per-unit = |:|x (b) What happens to annual units demanded for the product if the rm increases the perunit price from $25 to $26? From $43 to $44? 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 rm increases the perunit price from $25 to $26? units at $25 perunit = X units at $26 perunit = x [ii] What happens to annual units demanded for the product if the rm increases the perunit price from $43 to $44? units at $43 per-unit units at $44 perunit = I: X 3' {iii} What happens to annual units demanded for the product if the rm increases the perunit price from $65 to $66? units at $65 per-unit units at $66 per-unit I: I: X X [iv] What is the suggested relationship between the perunit price and annual demand for the product in units? This suggests that the relationship is linear V_ V and that annual demand 'falls v If by V units for elrerl.r $1 in price increase. (c) ShowI the mathematical model for the total revenue [TR] in terms of p, which is the annual demand multiplied by the unit price. TR: 5: (d) Based on other considelations, the rm's management will onlyr consider price alternatives of $28, $40r and $52. Use your model from part [b] to determine the price alternative that will maximize the total revenue. TR at $28 perunit = $ x TR at $40 perunit = 55 X TR at $52 perunit = $ x Given the constlaints, the Total Revenue is maximized at 1:: X perunit. (e) What are the expected annual demand and the total revenue corresponding to your recommended price? \":3: TR=$:x