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Oduvanchick [21]
2 years ago
14

Given the system of constraints name all vertices. Then find the maximum value of the given objective

Mathematics
1 answer:
larisa86 [58]2 years ago
3 0

Answer:

35

Step-by-step explanation:

The constraints are

The red line represents the function

y\leq \dfrac{1}{3}x+1

At y=0

0=\dfrac{1}{3}x+1\\\Rightarrow -1=\dfrac{1}{3}x\\\Rightarrow x=-3

At x=0

y=0+1\\\Rightarrow y=1

Two points are (-3,0),(0,1)

The blue line represents the function

5\geq y+x

at y=0

5=x

at x=0

y=5

Two points are (5,0),(0,5)

The other two constraints are x\geq 0, y\geq 0. So, the point has to be in the first quadrant

From the graph it can be seen there are two points where the function will be maximum let us check them.

(3,2)

7x-2y=7\times 3-2\times 2=17

(5,0)

7x-2y=7\times 5-2\times 0=35

So, the maximum value of the function is 35.

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