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3 years ago

7

HELP!!!! [HELP] A person can pay $43 for a membership to the art museum and then go to the museum for just $1 per visit. What is

the maximum number of visits a member of the art museum can make for a total cost of $50?

1 answer:

WITCHER [35]3 years ago

8 0

Answer:

Step-by-step explanation:

50= 1x+43

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This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the ex

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$L(x,y,z,\lambda)=10x+10y+2z+\lambda(5x^2+5y^2+2z^2-42)$

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$L_y=10+10\lambda y=0\implies1+\lambda y=0$

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$\begin{cases}L_x=0\\L_y=0\\L_z=0\end{cases}\implies1+\lambda x=1+\lambda y=1+2\lambda z=0\implies x=y=2z$

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$z^2=1\implies z=\pm1\implies x=y=\pm2$

There are two critical points, at which we have

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$f\left(-2,-2,-1\right)=-42\text{ (a minimum value)}$

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Let H = Hailey's age and M = Maverick

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Maverick is 12 years old. Hailey = 3M = 3(12) = 36 years old.

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