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1 year ago

The function C = x - 2y is maximized at the vertex point of the feasible region at (8, 2). What is the maximum value?

Mathematics

1 answer:

lubasha [3.4K]1 year ago

5 0

The required maximum value of the function C = x - 2y is 4.

Given that,
The function C = x - 2y is maximized at the vertex point of the feasible region at (8, 2). What is the maximum value is to be determined.

<h3>What is the equation?</h3>

The equation is the relationship between variables and represented as y =ax +m is an example of a polynomial equation.

Here,
Function C = x - 2y
At the vertex point of the feasible region at (8, 2)
C = 8 - 2 *2
C= 4

Thus, the required maximum value of the function C = x - 2y is 4.

Learn more about equation here:

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3 years ago

A new security system needs to be evaluated in the airport. The probability of a person being a security hazard is 4%. At the ch

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Step-by-step explanation:

Denote the events a follows:

$P$ = a person passes the security system

$H$ = a person is a security hazard

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$P (H) = 0.04,\ P(P^{c}|H^{c})=0.02\ and\ P(P|H)=0.01$

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$P(H^{c})=1-P(H)=1-0.04=0.96\\P(P|H^{c})=1-P(P|H)=1-0.02=0.98\\$

(a)

Compute the probability that a person passes the security system using the total probability rule as follows:

The total probability rule states that: $P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})$

The value of P (P) is:

$P(P)=P(P|H)P(H)+P(P|H^{c})P(H^{c})\\=(0.01\times0.04)+(0.98\times0.96)\\=0.9412$

Thus, the probability that a person passes the security system is 0.9412.

(b)

Compute the probability that a person who passes through the system is without any security problems as follows:

$P(H^{c}|P)=\frac{P(P|H^{c})P(H^{c})}{P(P)} \\=\frac{0.98\times0.96}{0.9412} \\=0.9996\\\approx1$

Thus, the probability that a person who passes through the system is without any security problems is approximately 1.

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