Using Lagrange multipliers, we have the Lagrangian
with partial derivatives (set equal to 0)
Substituting the first three equations into the fourth allows us to solve for
:
For each possible value of
, we get two corresponding critical points at
.
At these points, respectively, we get a maximum value of
and a minimum value of
.
Answer:
x = -3
, y = 0
Step-by-step explanation:
Solve the following system:
{4 x - y = -12 | (equation 1)
-x - y = 3 | (equation 2)
Add 1/4 × (equation 1) to equation 2:
{4 x - y = -12 | (equation 1)
0 x - (5 y)/4 = 0 | (equation 2)
Multiply equation 2 by 4/5:
{4 x - y = -12 | (equation 1)
0 x - y = 0 | (equation 2)
Multiply equation 2 by -1:
{4 x - y = -12 | (equation 1)
0 x+y = 0 | (equation 2)
Add equation 2 to equation 1:
{4 x+0 y = -12 | (equation 1)
0 x+y = 0 | (equation 2)
Divide equation 1 by 4:
{x+0 y = -3 | (equation 1)
0 x+y = 0 | (equation 2)
Collect results:
Answer: {x = -3
, y = 0
Answer:
SRO and QRO
Step-by-step explanation:
Hope this helps!
<span>12+3(8+x)
= 12 + 24 + 3x
= 3x + 36</span>
Year Net Profit
1 <span>$14,250.00
2 $15,390.00
3 $16,621.20
4 $17,950.90</span>2
We need to get the increase of the net profit of the current year from the previous year.
Percentage increase = (Current year - Previous Year)/ Previous Year * 100%
Year 2: (15,390 - 14, 250) / 14,250 * 100% = 0.08 * 100% = 8%
Year 3: (16,621.20 - 15,390) / 15,390 * 100% = 0.08 * 100% = 8%
Year 4: (17,950.90 - 16,621.20) / 16,621.20 * 100% = 0.08 * 100% = 8%
Every year the net income increases by 8%. So, the net income in Year 5 will be:
17,950.90 x 1.08 = 19,386.97 Choice D.
