A five-digit number has the digits 0,9 7, 0, and 2. To the nearest thousand, it rounds to 30,000. What is the number?

Solve the linear programming problem. Minimize and maximize Upper P equals negative 20 x plus 30 y Subject to 2 x plus 3 y great

Alika [10]

Answer:

Maximum = 540 at (6,14)

Minimum = 300 at (0,10) or (12,2).

Step-by-step explanation:

The given linear programming problem is

Minimize and maximize: P = 20x + 30y

Subject to constraint,

$2x+3y\ge 30$ .... (1)

$2x+y\le 26$ .... (2)

$-2x+3y\le 30$ .... (3)

$x,y\geq 0$

The related equation of given inequalities are

$2x+3y=30$

$2x+y=26$

$-2x+3y=30$

Table of values are:

For inequality (1).

x y

0 10

15 0

For inequality (2).

x y

0 26

13 0

For inequality (3).

x y

0 10

15 0

Pot these ordered pairs on a coordinate plane and connect them draw the corresponding related line.

Check each inequality by (0,0).

$2(0)+3(0)\ge 30\Rightarrow 0\ge 30$ False

$2(0)+(0)\le 26\Rightarrow 0\le 26$ True

$-2(0)+3(0)\le 30\Rightarrow 0\le 30$ True

It means (0,0) is included in the shaded region of inequality (2) and (3), and (0,0) is not included in the shaded region of inequality (1).

From the below graph it is clear that the vertices of feasible region are (0,10), (6,14) and (12,2).

Calculate the values of objective function on vertices of feasible region.

Point P = 20x + 30y

(0,10) P = 20(0) + 30(10) = 300

(6,14) P = 20(6) + 30(14) = 540

(12,2) P = 20(12) + 30(2) = 300

It means objective function is maximum at (6,14) and minimum at (0,10) or (12,2).

7 0

3 years ago

What is the surface area of this design ?<br><br> please help!!!!!!!!!!

Kay [80]

The surface area of the design is 5

4 0

3 years ago

Read 2 more answers

What is the value of x?

fiasKO [112]

Answer:

n math, value is a number signifying the result of a calculation or function. So, in the example above, you could tell your teacher that the value of 5 x 6 is 30 or the value of x + y if x = 6 and y = 3 is 9. Value can also refer to a variable or constant. ... A variable is a letter used to signify an unknown number.

4 0

3 years ago

Which fraction is less than 1 chose all of the correct answer, and explain why you chose and write it down and explain your answ

EleoNora [17]

Answer:

$(3/4)$ and $(2/3)$ .

Step-by-step explanation:

For a fraction of the form $(p / q)$ , the number in front of the division ( $p$ ) is the numerator. The number after the division ( $q$ ) is the denominator.

$\begin{aligned} \frac{p}{q} \quad \genfrac{}{}{0}{}{(\text{numerator})}{(\text{denominator})}\end{aligned}$ .

A positive fraction $(p/q)$ ( $p,\, q > 0$ ) is less than $1$ as long as the numerator $p$ is smaller than the denominator $q$ (that is, $p < q$ .) The reason is that as long as $p,\, q > 0$ :

$\begin{aligned} & \frac{p}{q} < 1 \\ \iff & (q)\, \left(\frac{p}{q}\right) < (q)\, (1) && (\text{given that $q > 0$}) \\ \iff & p < q\end{aligned}$ .

For example, in the fraction $(2/3)$ , $2$ is the numerator while $3$ is the denominator. Both the numerator and the denominator are positive, while the numerator $2\!$ is smaller than the denominator $3\!$ . Therefore, $(2/3)$ would be less than $1$ .

6 0

1 year ago

On every 3rd day Ivan goes to the gym to exercise. Every 5th day Gavin goes to the gym to exercise. What is the first day Ivan a

Colt1911 [192]

You have to find the LCM (least common multiple) of both numbers.

3: 3, 6, 9, 12, 15
5: 5, 10, 15

ivan and gavin will be together at the gym on the 15th day.

8 0

3 years ago

Read 2 more answers