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)
Answer is C because it is proportion.
Answer:
240
Step-by-step explanation:
So to do this problem, you have to find the area of each 2d figure. To start off, you need to find the top sides. (to make this easier I won't show the work)
<u>Green-</u> Top & bottom: 16. Sides (4): 28
<u>Pink-</u> Top & bottom: 8. Sides (4): 20
Now you add it all up.
32+112+16+80=240
<span>7(6x-4)+2x
=42x - 28 + 2x
= 44x - 28</span>
