Kyle is making 9 birdhouses. He uses 8 nails for each birdhouse. If Kyle has a box of 100 nails, how many nails will he have lef
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Answer:
(x,y)=(0,7.333)
Step-by-step explanation:
We are required to:
Maximize p = x + 2y subject to
- x + 3y ≤ 22
- 2x + y ≤ 14
- x ≥ 0, y ≥ 0.
The graph of the lines are plotted and attached below.
From the graph, the vertices of the feasible region are:
- (0,7.333)
- (4,6)
- (0,0)
- (7,0)
At (0,7.333), p=0+2(7.333)=14.666
At (4,6), p=4+2(6)=4+12=16
At (0,0), p=0
At (7,0), p=7+2(0)=7
Since 14.666 is the highest, the maximum point of the feasible region is (0,7.333).
At x=0 and y=7.333, the function p is maximized.
We'd rather not have x on both sides of the equation when trying to solve this. To eliminate the x on the right side, subtract both sides by x.
Let's get eliminate the "5" on the left side. Subtract both sides by 5.
To finish this, divide both sides by 4.
That is the answer. Hope this helps! :)