Question

Use the table below to create a nonlinear model based on the table to answer the following question(s). The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which plan to reduce their ticket rates. Atlas Movie Theater Ticketing Ticket Class Classic Silver Gold Current Rate Average Daily Sold Elasticity Price Range 8.45 150 -1.3 6.5 7.5 13.25 80 -2.25 11.5 12.5 17.5 30 -1.1 15.5 16.5 Total Capacity 300 According to the nonlinear model, which of the following is the projected revenue figure for Classic tickets based on its new price? O $1,314.72 $1521.68 $1,289.42 O $1,312.52

Answer 1

Answer: Revenue from the Classic model = $1,289.42

Excel model:

A B D E TT G H 1 2 Classic Silver Gold 3 4 5 6 7 8 Price Current price 8.45 Average demand 150 Elasticity -1.3 13.25 80 -2.25 17.5 30 -1.1 9 Change in price =C3-C4 =D3-D4 =E3-E4 Change in demand =C8*26*(C5/C4) =D8*D6*(D5/D4) =E8*E6*(E5/E4) Actual demand =C5+C9 =D5+D9 =E5+E9 =SUM(C10:E10) < 300 10 11 12 Revenue =C3*C10 =D3*D10 =E3*E10 =SUM(C12:E12) 13 14 15 Max price Min price 7.5 6.5 12.5 11.5 16.5 15.5 16

Solver inputs:

Set Objective: SE$13 To: Max Min O Value of: 0 By Changing Variable Cells: $C$3:$E$3 Subject to the Constraints: $C$3:$E$3 <= $C$15:$E$15 $C$3:$E$3 >= $C$16:$E$16 SF$10 <= $H$10 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: GRG Nonlinear Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

Solution:

Price Current price Average demand Elasticity Classic 7.5 8.45 150 -1.3 Silver 12.0581471 13.25 80 -2.25 Gold 16.5 17.50 30 -1.1 Change in price Change in demand Actual demand -0.95 21.92 171.92 -1.19 16.19 96.19 -1.00 1.89 31.89 300.00 300 Revenue 1,289.42 1,159.89 526.11 2,975.43 Max price Min price 7.50 6.50 12.50 11.50 16.50 15.50