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The director of a health clinic has a quarterly budget of $600,000. She
would like to allocate this budget to maximize the number of patient visits, P, which is
given as a function of the number of doctors, D, and the number of nurses, N, by
[tex]P=1000D^0^.^6N^0^.^3[/tex].

A doctor’s quarterly salary is $40,000; nurses is $10000.

Maximize the number of patient visits given the pay constraints.

Find the value of the LaGrange multiplier and interpret its meaning in this
problem.

Respuesta :

okpalawalter8

The meaning of this problem is that with 7 nurses they can only hire D=13.25

What is the meaning of this problem.?

Generally, the equation for the model is  mathematically given as

[tex]P=1000D^{0.6}N^{0.3}[/tex]

Therefore,

[tex]dv/dD=0.6*1000*D^{0.4}N)^{0.3}[/tex]

[tex]dv/dD=600* \frac{N6.1}{D6.1}=0[/tex]

Also

[tex]dv/dN=300* \frac{N6.8}{N6.7}=0[/tex]

Equations 1 and 2

[tex]300* \frac{D6.8}{N6.7}=600* \frac{N6.1}{D6.1}[/tex]

.sub D=(60N)/4

[tex]300* \frac{((60N)/4)6.8}{N6.7}=600* \frac{N6.1}{((60N)/4)6.1}[/tex]

N=6.67

N=7

solve for D

D=(60(7))/4

D=13.25

In conclusion, with 7 nurses they can only hire D=13.25

Read more about  LaGrange multiplier

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