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:
1. b
Step-by-step explanation:
This is completing the square:
(x^2+12x+36)+42-36
Answer: (x+6)^2 +6
Answer:
3 necklaces
Step-by-step explanation:
$40.50-$30.00=$10.50 Subtract her total money and cost of dress
$10.50-$3.50=$6.00 subtract each necklace price from remaining money
$6.00-$3.50=$3.50 keep subtracting price of necklace
$3.50-$3.50=$0 that was 3 necklaces
