Question 1: RAK Airlines has been told that it may schedule six flights per day

Question

Question 1: RAK Airlines has been told that it may schedule six flights per day departing from RAK international Airport. The destination of each flight may be Muscat, Dammam, or Doha-The table below shows the contribution to the company's profit from any given number of daily flights from RAK to each possible destination. Number of Planes 3 4 56 Muscat 80 50 210 250 270 2803-2 Destination Dammam | 100 | 195 | 275|325|30025 | 190 | 180 | 265 | 310 | 350 | 320 3-3-0 2- n:3 Doha Profit per Flight ) 1. Find the optimal number of flights that should depart RAK for each destination. 2. How would the answer change if the airline were restricted to only four daily flights? 3. RAK would like to operate a minimum of 2 flights to Doha. Find the optimal assignment

Explanation / Answer

1. We can see that the maximum profit is $350 per flight to Doha for 5 flights. Therefore, we have to choose atleast 5 flights for maximum profit. This will give a profit of $1750.

For the last flight, we can either choose 1 flight to Muscat for $80, to Damman for $100, or 1 additional flight to Doha for $320 - 5 * $30 = $170 for additional profit. Since the additonal flight to Doha gives maximum additional profit of $170, we operate the last flight also to Doha.

So, RAK operates all 6 flights to Doha for profit of $320 * 6 = $1920.

2. For maximum of 4 flights, we again check the table for maximum profit in the first 4 columns only. The maximum profit per flight is now $325 for 4 flights to Damman.

So, RAK operates all 4 flights to Damman for profit of $325 * 4 = $1500.

3. RAK has to operate atleast 2 flights to Doha.

For 6 flights, the answer remains the same as 1) as RAK was already operating all 6 flights to Doha for profit of $320 * 6 = $1920.

For 4 flights, we can now only consider first two columns for Muscat and Damman and 2nd, 3rd, and 4th columns for Doha. We now see that the maximum is $310 per flight for 4 flights to Doha.

So, RAK operates all 4 flights to Doha for profit of $310 * 4 = $1240.

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