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)
I disagree with her because for every 1 is six, it shouldn’t have +y on it that is just adding a number that is unneeded
The answer to this question is x=8; y= -7
Answer:
We know that the kite with the tail is 15 feet and 6 inches. While 6 inches is 0,50 foot, it's 15,5 feet. If the lenght of the kite is x, then:
15,5 = x + 1,5 + 2x
15,5 = 3x + 1,5 / - 1,5 (both sides)
14 = 3x / : 3 (both sides)
x ≈ 4,66
The kite is approx .4,66 feet long. It means that the tail is about 15,5 - 4,66 = 10,84 feet long.
