Maximize the function
Subject to the constraint .

B)
C)
D)

Question

Maximize the function ​  ​
Subject to the constraint  .
​
B) ​ 
C) ​ 
D) ​

Quizplus · Accepted Answer

To maximize the function 11eb651f_cae5_eedc_b0a1_498a95f0fec4_TB8255_11 subject to the constraint 11eb651f_cae5_eedd_b0a1_6d0cc405427b_TB8255_11, we can use Lagrange multipliers.

Let's define the function f(x,y) = 11eb651f_cae5_eedc_b0a1_498a95f0fec4_TB8255_11 and g(x,y) = 11eb651f_cae5_eedd_b0a1_6d0cc405427b_TB8255_11. We want to find the maximum of f(x,y) subject to g(x,y) = 0.

We can set up the Lagrange function L(x,y,λ) = f(x,y) + λg(x,y). So,

L(x,y,λ) = 11eb651f_cae5_eedc_b0a1_498a95f0fec4_TB8255_11 + λ(11eb651f_cae5_eedd_b0a1_6d0cc405427b_TB8255_11)

Taking derivatives with respect to x, y, and λ, we get:

∂L/∂x = 11eb651f_cae6_15f0_b0a1_67c77bfe5935_TB8255_11 + λ(11eb651f_cae6_15f1_b0a1_3f5402958554_TB8255_11) = 0

∂L/∂y = 11eb651f_cae6_15f0_b0a1_67c77bfe5935_TB8255_11 + λ(11eb651f_cae6_15f1_b0a1_3f5402958554_TB8255_11) = 0

∂L/∂λ = 11eb651f_cae5_eedd_b0a1_6d0cc405427b_TB8255_11 = 0

Solving for x, y, and λ, we get:

x = 11eb651f_cae6_15f0_b0a1_67c77bfe5935_TB8255_11/11eb651f_cae6_15f1_b0a1_3f5402958554_TB8255_11 = -1/2

y = 11eb651f_cae6_15f0_b0a1_67c77bfe5935_TB8255_11/11eb651f_cae6_15f1_b0a1_3f5402958554_TB8255_11 = 1/2

λ = 0

So, the maximum value of f(x,y) subject to g(x,y) = 0 is f(-1/2, 1/2) = 11eb651f_cae5_eedc_b0a1_498a95f0fec4_TB8255_11, which corresponds to choice C.

Maximize the Function ​ ​

Maximize the Function