Answer:
The objective function in terms of one number, x is
S(x) = 4x + (12/x)
The values of x and y that minimum the sum are √3 and 4√3 respectively.
Step-by-step explanation:
Two positive numbers, x and y
x × y = 12
xy = 12
S(x,y) = 4x + y
We plan to minimize the sum subject to the constraint (xy = 12)
We can make y the subject of formula in the constraint equation
y = (12/x)
Substituting into the objective function,
S(x,y) = 4x + y
S(x) = 4x + (12/x)
We can then find the minimum.
At minimum point, (dS/dx) = 0 and (d²S/dx²) > 0
(dS/dx) = 4 - (12/x²) = 0
4 - (12/x²) = 0
(12/x²) = 4
4x² = 12
x = √3
y = 12/√3 = 4√3
To just check if this point is truly a minimum
(d²S/dx²) = (24/x³) = (8/√3) > 0 (minimum point)
You have to consider the “ends” of the x-axis, the far right (for infinitely large values of x) and left (for infinitely small values of x) of the graph.
From the diagram above you can see that:
- When
then 
(notice that as the values of x get smaller and smaller, the graph gets closer and closer to the line y=1); - When
then 
(notice that as the values of x get larger and larger, the graph gets closer and closer to the line y=1).
Answer: correct choice is D.
Answer:
4y^2-12y
Step-by-step explanation:
y^2+4y-16y+3y^2
=y^2+3y^2+4y-16y
=4y^2+4y-16y
=4y^2-12y
He can only pick 7 different groups because 2 times 7 is 14, and there are 15 people in all.
Hope this helps. c:
P = -16
Subtract 7 from both sides to isolate the variable.
