Find the minimum value of the function for the polygonal convex set determined by the given system of inequalities.
1 answer:
Answer:
Option b (4,1)
Step-by-step explanation:
The region given by the system of inequalities is shown in the graph. We must look within this region for the point that minimizes the objective function
The minimum points are found in the lower vertices of the region.
These vertices are found by equating the equations of the lines::
-------------------
---------------------
The lower vertices are:
(4, 1) (2, 4)
Now we substitute both points in the objective function to see which of them we get the lowest value of
Then the value that minimizes f(x, y) is (4,1).
Option b
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Answer:
There are 118 plants that weight between 13 and 16 pounds
Step-by-step explanation:
For any normal random variable X with mean μ and standard deviation σ : X ~ Normal(μ, σ)
This can be translated into standard normal units by :
Let X be the weight of the plant
X ~ Normal( 15 , 1.75 )
To find : P( 13 < X < 16 )
= P( -1.142857 < Z < 0.5714286 )
= P( Z < 0.5714286 ) - P( Z < -1.142857 )
= 0.7161454 - 0.1265490
= 0.5895965
So, the probability that any one of the plants weights between 13 and 16 pounds is 0.5895965
Hence, The expected number of plants out of 200 that will weight between 13 and 16 = 0.5895965 × 200
= 117.9193
Therefore, There are 118 plants that weight between 13 and 16 pounds.