Explanation Given Information: The provided function is f = 5 x + 2 y and the figure is, Calculation: Consider the three equations in the figure. Solve the three equations to find the point of intersections. First take the equations, x + y = 9 …… (1) 4 x + y = 12 …… (2) Subtract equation (1) from (2), 3 x = 3 x = 1 Put x = 1 in equation (1), 1 + y = 9 y = 8 Therefore, ( 1 , 8 ) is the point of intersection of the equations x + y = 9 and 4 x + y = 12 . Now take the equations, x + y = 9 …… (3) x + 3 y = 15 …… (4) Subtract equation (3) from (4), 2 y = 6 y = 3 Put y = 3 in equation (3), x + 3 = 9 x = 6 Therefore, ( 6 , 3 ) is the point of intersection of the equations x + y = 9 and x + 3 y = 15 . Now take the equation 4 x + y = 12 . Put x = 0 then y = 12 therefore y − intercept is ( 0 , 12 ) . Now take the equation x + 3 y = 15 . Put y = 0 , then x = 15 therefore x − intercept is ( 15 , 0 )

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 4, Problem 5T

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To calculate: The minimum and maximum values of the function f=5x+2y subject to the constraints determined by the shaded region in the graph shown below:

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One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs \[36\] \[20\] \[56\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] problem 1 Find the probability that a randomly selected student prefers dogs.Enter your answer as a fraction or decimal. \[P\left(\text{prefers dogs}\right)=\] Incorrect Check Hide explanation Preference Male Female TOTAL Prefers dogs \[\blueD{36}\] \[\blueD{20}\] \[\blueE{56}\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] There were \[\blueE{56}\] students in the sample who preferred dogs out of \[100\] total students.

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The minimum and maximum values of the function f = 5 x + 2 y subject to the constraints determined by the shaded region in the graph shown below:

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To calculate: The minimum and maximum values of the function f=5x+2y subject to the constraints determined by the shaded region in the graph shown below:

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