boitshupoO
2021-02-19
Answered

Multivariable optimization question. Find three positive real numbers whose sum is one and the sum of their squares is a minimum.

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2k1enyvp

Answered 2021-02-20
Author has **94** answers

Let the three positive real numbers be x,y and z.

then,

let sum of squares be:

put z in above function

Partially differenting the function g(x,y) and finding the critical points:

From the above two equtioan, we get:

Putting the value of x and y in

Using the second derivative test:

Since

Therefore, the sum of squarers will be minimom if

asked 2021-02-05

Use polar coordinates to find the limit. [Hint: Let $x=r\mathrm{cos}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}y=r\mathrm{sin}$ , and note that (x, y) (0, 0) implies r 0.]
$\underset{(x,y)\to (0,0)}{lim}\frac{{x}^{2}-{y}^{2}}{\sqrt{{x}^{2}+{y}^{2}}}$

asked 2021-09-08

Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.

$P\left(x\right)=-12{x}^{2}+2136x-41000$

To maximize the monthly rental profit , how many units should be rented out?

What is the maximum monthly profit realizable?

To maximize the monthly rental profit , how many units should be rented out?

What is the maximum monthly profit realizable?

asked 2020-11-27

Comsider this, multivariable fucntion

$f(x,y)=3xy-{x}^{2}+5{y}^{2}-25$

a)What is the value of f(-1,3)?

b)Find all x-values such that f(x,x)=0

a)What is the value of f(-1,3)?

b)Find all x-values such that f(x,x)=0

asked 2021-11-22

Find the solution set for the system

${x}^{2}+{y}^{2}=25$

$25{x}^{2}+{y}^{2}=25$

by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

asked 2021-09-05

Use the following linear regression equation to answer the questions.

(a) Which variable is the response variable?

(b) Which number is the constant term? List the coefficients with their corresponding explanatory variables.

(c) If

(d) Explain how each coefficient can be thought of as a "slope" under certain conditions.

asked 2021-11-22

A commodity has a demand function modeled by $p=126-0.5x$ and a total cost function modeled by $C=50x+39.75$ , where x is the number of units.

(a)Use the first marginal analysis criterion presented in class to find the production level that yields a maximum profit. Then use the second criterion to ensure that level yields a maximum and not a minimum. Finally, what unit price (in dollars) yields a maximum profit?

$ per unit

(b)When the profit is maximized, what is the average total cost (in dollars) per unit? (Round your answer to two decimal places.)

$ per unit

(a)Use the first marginal analysis criterion presented in class to find the production level that yields a maximum profit. Then use the second criterion to ensure that level yields a maximum and not a minimum. Finally, what unit price (in dollars) yields a maximum profit?

$ per unit

(b)When the profit is maximized, what is the average total cost (in dollars) per unit? (Round your answer to two decimal places.)

$ per unit

asked 2021-09-16

Find the complex zeros of the following polynomial function. Write f in factored form.

$f\left(x\right)={x}^{3}-12{x}^{2}+49x-58$

The complex zeros of f are =?

The complex zeros of f are =?