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3 years ago

Find the maximum value of P=3x+2y subject to the following constraints: Please help me!!!

Mathematics

1 answer:

UkoKoshka [18]3 years ago

6 0

Answer:

maximum value of P is 33

Step-by-step explanation:

Sketch the lines represented by the constraints

5x + y = 16

with intercepts ( $\frac{16}{5}$ , 0) and (0, 16)

2x + 3y = 22

with intercepts (11, 0) and (0, $\frac{22}{3}$ )

The solutions to both are below the lines.

Solve 5x + y = 16 and 2x + 3y = 22 simultaneously to find the point of intersection at (2, 6)

The coordinates of the vertices of the feasible region are

(0, 0), (0, 16), (2, 6), 11, 0)

Evaluate the objective function at each vertex

P = 3(0) + 2(0) = 0 + 0 = 0

P = 3(0) + 2(16) = 0 + 32 = 32

P = 3(2) + 2(6) = 6 + 12 = 18

P = 3(11) + 2(0) = 33 + 0 = 33

The maximum value of P is 33 when x = 11 and y = 0

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The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the

gladu [14]

Answer:

Part 1) Australia $19,751,012\ people$

Part 2) China $1,319,645,764\ people$

Part 3) Mexico $109,712,539\ people$

Part 4) Zaire $60,534,681\ people$

Step-by-step explanation:

we know that

The equation of a exponential growth function is given by

$P(t)=a(1+r)^t$

where

P(t) is the population

t is the number of years since year 2000

a is he initial value

r is the rate of change

Part 1) Australia

we have

$a=19,169,000\\r=0.6\%=0.6\100=0.006$

substitute

$P(t)=19,169,000(1+0.006)^t$

$P(t)=19,169,000(1.006)^t$

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

$P(5)=19,169,000(1.006)^5=19,751,012\ people$

Part 2) China

we have

$a=1,261,832,000\\r=0.9\%=0.9\100=0.009$

substitute

$P(t)=1,261,832,000(1+0.009)^t$

$P(t)=1,261,832,000(1.009)^t$

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

$P(5)=1,261,832,000(1.009)^5=1,319,645,764\ people$

Part 3) Mexico

we have

$a=100,350,000\\r=1.8\%=1.8\100=0.018$

substitute

$P(t)=100,350,000(1+0.018)^t$

$P(t)=100,350,000(1.018)^t$

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

$P(5)=100,350,000(1.018)^5=109,712,539\ people$

Part 4) Zaire

we have

$a=51,965,000\\r=3.1\%=3.1\100=0.031$

substitute

$P(t)=51,965,000(1+0.031)^t$

$P(t)=51,965,000(1.031)^t$

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

$P(5)=51,965,000(1.031)^5=60,534,681\ people$

8 0

3 years ago

Anyone know this by chance?

zaharov [31]

Answer:

The idea of circumference and diameter should be withheld.

Step-by-step explanation:

The idea of circumference and diameter should be withheld.

8 0

3 years ago

PLEASE HELP ME I BEG YOU

Rus_ich [418]

You need to find "two-fifths of 30." Of here means multiplication:

$\begin{aligned}\dfrac{2}{5}\cdot 30 &= \dfrac{2}{5}\cdot\dfrac{30}{1}\\[0.5em] &= \dfrac{60}{5}\\[0.5em] &= 12\end{aligned}$

There are 12 athletes in the club.

5 0

2 years ago

Read 2 more answers

Janice deposited $750 in a savings account that earns 3.5% simple interest. How much interest has Janice earned by the end of th

Ronch [10]

Janice deposited $750 and a savings account earns 3.5% simple interest.
r = 3.5% = 0.035
I = $750 * 0.035
I = $26.25
Answer:
Janice has earned
D ) $26.25

8 0

3 years ago

Which expression has the same value as 5(4x+4)

aev [14]

Answer: 20x + 20

Step-by-step explanation: In this problem, the 5 "distributes" through the parentheses, multiplying by each of the terms inside.

So we have 5(4x) + 5(4) which simplifies to 20x + 20.

8 0

3 years ago