You're looking for the extreme values of  subject to
 subject to  . The Lagrangian is
. The Lagrangian is

with critical wherever the partial derivatives vanish:




Substituting the first three solutions into the last equation gives



At these points, we have


so the highest temperature the bee can experience is 28º F at the point (1, 2, -2), and the lowest is -26º F at the point (-1, -2, 2).
 
        
             
        
        
        
I think 4 most likely because if u take the middle of the 3 dots it would lave the last dot on the 4
        
             
        
        
        
Answer:
6 of x and 5 of y
Step-by-step explanation:
x = number of closets of the first type
y = number of closets of the second type
1200 = 100x + 120y
100 = 10x + 8y
10x = 100 - 8y
10x(100 - 8y) + 120y = 1200
1000 - 80y + 120y = 1200
40y = 200
y = 5
100 = 10x + 8×5 = 10x + 40
60 = 10x
x = 6
20x + 24y = max
20×6 + 24×5 = 120 + 120 = 240
 
        
             
        
        
        
I don't know if I'm right, but if each pencil is 10.5 grams then you multiply it by 5 ( number of pencils) and you get 52.5, which would not meet the standards of a pack weighing 60 to 95 grams.