Explanation Given: The data analyzed by executives at Federal Express: Boeing 727(Type 1) Falcon 20(Type 2) Direct operating cost $1400 per hour $500 per hour Payload 42,000 pounds 6000 pounds Calculation: To compute the number of each type of aircraft and to maximize the number of aircrafts, use the two steps as follows: Let x be the number of Boeing 727 s aircraft and y be the number of Falcon 20 aircraft. Thus, the objective function based on x and y is as shown below: z = x + y According to the statement the inequality representing the first constraint is: the operating cost of Boeing 727 s aircraft is $ 1400 and Falcon 20 aircraft is $ 500 per hour. Also, the total cost cannot exceed the $ 35000 Hence, the inequality representing constraint is shown below: 1400 x + 500 y ≤ 35 , 000 According to the statement the inequality representing the second constraint is:the payload of Boeing 727 s aircraft is 42000 pounds and Falcon 20 aircraft is 6000 pounds. Also, the total cannot be less than $ 672 , 000 pounds. Hence, the inequality representing constraint is shown below: 1400 x + 500 y ≤ 35 , 000 According to the statement the inequality representing the third constraint is:that only 20 Boeing 727 s aircrafts are available. Hence, the inequality representing constraint is shown below: x ≤ 20 Consider the first inequality constraint 1400 x + 500 y ≤ 35 , 000 , to solve this take it as an equality 1400 x + 500 y = 35 , 000 Put x = 0 in the equation and find the value of y- intercept: 1400 x + 500 y = 35 , 000 0 + 500 y = 35 , 000 y = 70 So, the intercepts of the line are ( 0 , 70 ) . Now, put y = 0 in the equation and find the value of x -intercept: 1400 x + 500 y = 35 , 000 1400 x + 0 = 35 , 000 x = 25 So, the intercepts are ( 25 , 0 ) . Now take ( 0 , 0 ) as a test point and put it in the inequality and if the inequality holds then shade the area towards test point. 1400 x + 500 y ≤ 35 , 000 0 + 0 ≤ ? 35 , 000 0 ≤ 35 , 000 Since the test point satisfies the inequality, shade the region towards the origin. Similarly, Consider the second inequality constraint 42 , 000 x + 6000 y ≥ 672 , 000 , to solve this take it as an equality as shown below: 42 , 000 x + 6000 y = 672 , 000 Put x = 0 in the equation and find the value of y- intercept: 42 , 000 x + 6000 y = 672 , 000 0 + 6000 y = 672 , 000 y = 112 So, the intercepts are ( 0 , 112 )

5th Edition

ISBN: 9780321837240

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 8.6, Problem 23E

To determine

To calculate: The number of each type of aircraft that should federal Express have purchased to maximize the number of aircrafts. There are two options available to Federal Express, one is 20 Boeing 727 s and the French built Dassault Fanjet Falcon 20. The constraints faced by Federal Express are that the hourly operating cost was limited to $35,000, Total payload had to be at least 672,000 pounds and only 20727 s were available.

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Chapter 8.6, Problem 22E

Chapter 8.6, Problem 24E

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