First, graph the three inequalities: x ≥ 5 , y ≤ 10 , 2x - y ≤ 8
Next, look for the 3 intersections (vertices) of the lines: (5, 2) , (5, 10) , (9, 10)
Finally, input the vertex coordinates into P = 4x + 5y and look for the biggest #.
(5, 2): 4(5) + 5(2) = 20 + 10 = 30
(5, 10): 4(5) + 5(10) = 20 + 50 = 70
(9, 10): 4(9) + 5(10) = 36 + 50 = 86
Answer: maximum profit = 86
Please further explain your question...
To find the answer, you have to figure out the y-intercept and the slope.
The y-intercept is relatively easy. Look at the graph and locate the spot where the line passes the y axis. It passes at (0, 2), which means that the y-intercept is 2. So, we can eliminate two of the answers.
Now, on to the slope. Slope is the change in y over the change in x, or rise over run. We need at least two points to find the slope. The most obvious ones are the intercepts: (0, 2) and (-1, 0).
Change in y is the difference of the y coordinates: 2 - 0 = 2.
Change in x is the difference of the x coordinates, but this subtraction must be in the same order as the difference of the y coordinates: 0 - (-1) = 1
Change in y over change in x is:
2/1 = 2
So, the slope is 2.
Taking the whole problem, the equation in slope-intercept form is: y = 2x + 2.
The answer is D.
