Assignment Marketing Analysis

COMM 414) Assignment #3

1.1

How many possible schedule combinations are there for Kerridale Theatre?

Total number of Possible Ways with only regular movies

COMBIN(5, 4) * (3^4) + COMBIN(5, 3) * (3^3) + COMBIN(5, 2) * (3^2) + COMBIN(5,1 ) * 3 )

Combinations with IMAX movies, given that Doctor Strange can only be 

(COMBIN(2,1) * (2+3+3+3) + COMBIN(2,2) * (3^3))

=( COMBIN(5, 4) * (3^4) + COMBIN(5, 3) * (3^3) + COMBIN(5, 2) * (3^2) + COMBIN(5,1 ) * 3 ) + (COMBIN(2,1) * (2+3+3+3) + COMBIN(2,2) * (3^3) )

= 829 

1.2 

What is the expected revenue from movie ticket sales? 

Expected Revenue = $5885.691

What is the probability that the revenue target will be equal to or greater than $6,000?

Probability = (3316/10000) x 100% = 33.16%

Using following R code: 

revenuePred <- function(n=1000, lambda=400)

{

  # step 1, simulate number of people arriving

  total = rpois(n, lambda)

  # step 2, calculate demand

  demand_doc = round(total*0.4)

  demand_arr = round(total*0.4)

  demand_acc = round(total*0.2)

  # step 3, calculate revenue

  revenue_doc = 19.99*pmin(demand_doc, 240)

  revenue_arr = 12.99*pmin(demand_arr, 160)

  revenue_acc = 12.99*pmin(demand_acc, 50)

  revenue = revenue_doc + revenue_arr+ revenue_acc

  return(revenue)

}

  m1 = revenuePred(10000,400)

  # Find expected revenue with mean function

  mean(m1)

  # Compare if m1 > $6000

  length(m1[m1 >= 6000])

1.3

Can you come out with another schedule that would improve the expected revenue?

No, it is not possible. 

However, there are four suggestions which we can provide to improve the revenue output. As the revenue function is R=P*Q then to increase revenue we can:    

    1. Increasing the price per movie.

    2. Changing the demand (by increasing total amount of people coming).

    3. Increasing capacity of theatre rooms.

    4. Shift distribution of demand preferences (by making people prefer more expensive movies)

    5. Change movie offering (ex. create IMAX version for popular movies, add IMAX capability to regular screens)

How likely is Sarah going to meet her target of 6,000, based on your schedule?

Based on our generated values in R, there is only a 33% chance that is possible. This percentage can increase however, as the values in R can change with random generalization.

2.1 

What specific mathematical programming problem the question belongs to? Write down the objective function.

This is a linear programming problem. 

In simplistic terms, the objective function is maximizing  revenue = ticketsales*ticket price. When expanded, the objective function is as follows:

revenue = (ticketsales_A x ticketprice_DS) + (ticketsales_A x ticketprice_AR)+(ticketsales_A x ticketprice_AC) + (ticketsales_B x ticketprice_DS) + (ticketsales_B x ticketprice_AR) + (ticketsales_B x ticketprice_AC) + (ticketsales_C x ticketprice_DS) + (ticketsales_C x ticketprice_AR) + (ticketsales_C x ticketprice_AR)

Write down the constraints.

• Ticketsales_A <= 120
• Ticketsales_B <= 120
• Ticketsales_C <= 120
• Ticketsales_D <= 80
• Ticketsales_E <= 50
• Ticketsales_DS <= Demand_DS <= 160
• Ticketsales_AR <= Demand_AR <= 160
• Ticketsales_AC <= Demand_AC <= 80

In binary terms (after setting up the problem in R):

• con1 = c(1,1,1,0,0,0,0,0,0,0,0,0,0,0,0)<= 1, 

meaning there must be at most 1 movie shown in screen A

• con2 = c(0,0,0,1,1,1,0,0,0,0,0,0,0,0,0)<= 1, 

meaning there must be at most 1 movie shown in screen B

• con3 = c(0,0,0,0,0,0,1,1,1,0,0,0,0,0,0)<= 1, 

meaning there must be at most 1 movie shown in screen C

• con4 = c(0,0,0,0,0,0,0,0,0,1,1,1,0,0,0)<= 1, 

meaning there must be at most 1 movie shown in screen D

• con5 = c(0,0,0,0,0,0,0,0,0,0,0,0,1,1,1)<= 1, 

meaning there must be at most 1 movie shown in screen E

• con6 = c(1,0,0,1,0,0,1,0,0,1,0,0,1,0,0) >= 1, 

meaning there must be at least 1 screening of Doctor Strange

• con7 = c(0,1,0,0,1,0,0,1,0,0,1,0,0,1,0)>= 1, 

meaning there must be at least 1 screening of The Arrival

• con8 = c(0,0,1,0,0,1,0,0,1,0,0,1,0,0,1)>= 1, 

meaning there must be at least 1 screening of The Accountant

2.2

Write out the R code and put the solution in a table. What is the total revenue from your optimized schedule?

library(lpSolve)

movie_obj = c(120*19.99,120*12.99,80*12.99,

              40*19.99,120*12.99,80*12.99,

              40*12.99,40*12.99,80*12.99,

              40*12.99,40*12.99,0*12.99,

              0*12.99,40*12.99,0*12.99)

con1 = c(1,1,1,0,0,0,0,0,0,0,0,0,0,0,0)

con2 = c(0,0,0,1,1,1,0,0,0,0,0,0,0,0,0)

con3 = c(0,0,0,0,0,0,1,1,1,0,0,0,0,0,0)

con4 = c(0,0,0,0,0,0,0,0,0,1,1,1,0,0,0)

con5 = c(0,0,0,0,0,0,0,0,0,0,0,0,1,1,1)

con6 = c(1,0,0,1,0,0,1,0,0,1,0,0,1,0,0)

con7 = c(0,1,0,0,1,0,0,1,0,0,1,0,0,1,0)

con8 = c(0,0,1,0,0,1,0,0,1,0,0,1,0,0,1)