Automobile traffic from three highways, H1, H2, and H3 must stop and wait for a green light before exiting to a toll road. The tolls are $3, $4, and $5 for cars existing from H1, H2, and H3, respectively. The flow rates from H1, H2, and H3 are 500, 600, and 400 cars per hours. The traffic light cycle may not exceed 2.2 min, and the green light on any highway must be on for at least 25 seconds. The yellow light is on for 10 seconds. The toll gate can handle a maximum of 510 cars per hour. Assuming that no cars move on yellow, determine the optimal green time interval for the three highway that will maximize toll gate revenue per traffic cycle.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

y > 1/3x

y < = -x + 4

hope this : )

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

the answer is two. hope this !