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Maurinko [17]
3 years ago
11

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
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