Expert: Scott A Wilson - 9/5/2011

Question
An airline with 2 types of airplanes, p and q, has contracted with a tour group to provide transportation for a minimum of 2000 first class, 1500 tourist class, and 2400 economic class passengers. For a certain trip, airplane p costs $12000 to operate and can accommodate 40 first class, 40 tourist class, and 120 economic class passengers, whereas airplane q costs $10000 to operate and can accommodate 80 first class, 30 tourist class, and 40 economic class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

Answer
I have included the answer as an attachment.
First, choose the most negative element in the top row (-2400 first time).
Next, take the value of each equation on the right and didide by the value under the -2400.
IN the 1st case, there was 12000/120 = 100 and 10,000/40 = 250.  Since 100 is the smaller of these two, use 120 in the 1st row as the pivot value.  Divide the row by this value,
making that value be 1.  Next, zero out -2400 in the top row and the 40 in the row below by adding the appropriate multiplier of the row a 1 was just put in.

If you're wondering where the value is that is picked in one table,
look for where the 1 is in the next table.