Find the maximum value of
1 answer:
Answer:
(3, 1)
Step-by-step explanation:
Given the following constraints:
2x + 4y ≤ 10
x + 9y ≤ 12
x ≥ 0
y ≥ 0
We have to first graph the above constraints and secondly, we find the boundary points for the feasible region. This is done by plotting the graphs of 2x + 4y ≤ 10 and x + 9y ≤ 12.
From the graph, the following points satisfy the constraints:
(0,0) , (3,1) , (0,4/3) , (5,0)
Given that:
P = x + 6y
For (0, 0): P = x + 6y = 0 + 6(0) = 0
For (3, 1): P = x + 6y = 3 + 6(1) = 9
For (0, 4/3) P = x + 6y = 0 + 6(4/3) = 8
For (5, 0) P = x + 6y = 5 + 6(0) = 5
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For this case, the full length of the log is equal to 1.
Therefore, the remaining length, we can obtain it by means of the following expression:
Rewriting we have:
Then, subtracting both numbers we have:
Answer:
The remaining amount of log is given by:
The slope of CD is 2
Step-by-step explanation:
The transformation done is dilation and the Dilation preserves the parallel lines that means that the image line C'D' of the line CD are parallel to each other and their slopes are same. so we have to find the slope of CD.
If the line is passing through the points (x1, y1) and (x2, y2), the slope is
From the diagram the coordinates of points C and D are :
C(5, 4), D(4, 2).
Thus, the slope of CD is
= 2
Hence, The slope of CD is 2, it does not change after dilation.