Answer:
x > 2
Step-by-step explanation:
![5x + 1 \div 3(3x + 6) > 14](https://tex.z-dn.net/?f=5x%20%2B%201%20%5Cdiv%203%283x%20%2B%206%29%20%3E%2014)
![5x + \frac{1}{3} \times 3(x + 2) > 14](https://tex.z-dn.net/?f=5x%20%2B%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%5Ctimes%203%28x%20%2B%202%29%20%3E%2014)
![5x + (x + 2) > 14](https://tex.z-dn.net/?f=5x%20%2B%20%28x%20%2B%202%29%20%3E%2014)
![5x + x + 2 > 14](https://tex.z-dn.net/?f=5x%20%2B%20x%20%2B%202%20%3E%2014)
![6x + 2 > 14](https://tex.z-dn.net/?f=6x%20%2B%202%20%3E%2014)
![6x > 14 - 2](https://tex.z-dn.net/?f=6x%20%3E%2014%20-%202)
![6x > 12](https://tex.z-dn.net/?f=6x%20%3E%2012)
![x > 2](https://tex.z-dn.net/?f=x%20%3E%202)
B is the Y-intercept or where the graph crosses the y-axis. they provide you with a few things which can help you figure this out. they give you the values of x and y in a table
X | Y
2 | -5
4 | -9 The difference between each Y value is 4...so, I add 4 to the -5
6 | -13 and get -1...going up another value for the X would be at 0. This leaves me with an ordered pair of (0,-1).....thus, the value of b is -1.
These are the important equations:
(1) q = 0.4x0.6y
(2) r = 26000x + 365y (r is the annual operating costs)
Since q is given (q=1000), we can express y in terms of x:
1000 = 0.4x0.6y
y = 1000/[(0.4x)(0.6)]
y = 12500/3x ----> we substitute this to equation 2
r = 26000x + 365(12500/3x)
r = 26000x + 1520833.33x^-1
r should be minimized. In calculus, we differentiate this and equate to zero. Then we can determine x, which is the number of employees.
dr/dx = 26000x - 1520833.33x^-2 = 0
1520833.33/x^2 = 26000
26000x^2 = 1520833.33
x^2 = 58.4935
x = 7.6
x=8
Thus, you should employ 8 employees to produce 1,000 automobiles a year with a minimum annual operating cost.