Explanation Given Information: There is a set up for a problem for Fly-by-Night Airlines with the unknowns x and y , where x represents the number of first-class tickets and y represents the number of business class. Consider the provided condition: There is a set up for a problem for Fly-by-Night Airlines with the unknowns x and y , where x represents the number of first-class tickets and y represents the number of business class. Numerically, this implies that there are infinitely many conceivable solutions: one for each point along the line joining the two corner points in the given condition. Select only those points with integer solutions that are in the feasible region and near this line and then pick the one that gives the biggest profit. The profit is largest on the corner points always. This is a proven fact. Consider the example: Let say the number of tickets be x for first class ticket in the flight and y tickets for the business ticket. Assume that the profit on each first-class ticket and the business ticket is $10 and $20 respectively. And there is maximum of 100 seats in the flight. Also, it is mandatory to have number of business seats twice than the first-class ticket. Now, the profit function will be P = 10 x + 20 y . Now, the number of tickets can be zero or greater than zero. That is, x ≥ 0 , y ≥ 0 There is a total of 100 seats in the flight that gives x + 2 y ≤ 100 So, the constraints are: x + 2 y ≤ 100 x ≥ 0 , y ≥ 0 For the equation, x + 2 y = 100 For x = 0 , 0 + 2 y = 100 y = 100 2 y = 50 Therefore, the point is ( 0 , 50 ) For y = 0 , x + 2 ( 0 ) = 100 x = 100 Therefore, the point is ( 100 , 0 ) . The graph of the equation x + 2 y = 100 is, The inequalities x ≥ 0 and y ≥ 0 represent the first quadrant only, hence neglect the other quadrants

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 6.2, Problem 63E

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The explanation how can it be interpreted if there are two corner points to maximize the profit when there is a set up for a problem for Fly-by-Night Airlines with the unknown variables x and y, where x represents the number of first-class tickets and y represents the number of business class.

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Chapter 6.2, Problem 62E

Chapter 6.2, Problem 64E

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Finite Mathematics and Applied Calculus (MindTap Course List)

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The explanation how can it be interpreted if there are two corner points to maximize the profit when there is a set up for a problem for Fly-by-Night Airlines with the unknown variables x and y , where x represents the number of first-class tickets and y represents the number of business class.

Solution Summary: The author explains that there are infinitely many conceivable solutions for a problem for Fly-by-Night Airlines with the unknown variables x and y.

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The explanation how can it be interpreted if there are two corner points to maximize the profit when there is a set up for a problem for Fly-by-Night Airlines with the unknown variables x and y, where x represents the number of first-class tickets and y represents the number of business class.

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