Please help, I don’t understand this. Will give brainliest

Please Help ASAP! Will name Brainliest! Question: Minimize the objective function P = 5x + 8y for the given constraints. x ≥ 0 y

maksim [4K]

Answer:

Option D.

Step-by-step explanation:

Minimize the objective function P = 5x + 8y for the given constraints.

$x\geq 0,y\geq 0$

$2x+3y\geq 15$

$3x+2y\geq 15$

The related equations of above inequalities are

$2x+3y=15$

$3x+2y=15$

For $2x+3y=15$ ,

x y

0 5

7.5 0

Plot (0,5) and (7.5,0) and join them by straight line.

For $3x+2y=15$ ,

x y

0 7.5

5 0

Plot (0,7.5) and (5,0) and join them by straight line.

Check the inequalities for (0,0).

$2(0)+3(0)\geq 15\Rightarrow 0\geq 15$ False

$3(0)+2(0)\geq 15\Rightarrow 0\geq 15$ False

It means both lines are solid lines and shaded region for each lies opposite side of (0,0).

From the below graph it is clear that the vertices of feasible region are (0,7.5), (3,3), (7.5,0).

Point P = 5x + 8y

(0,7.5) P=5(0)+8(7.5)=60

(3,3) P=5(3)+8(3)=15+24=39

(7.5,0) P=5(7.5)+8(0)=37.5 (Minimum)

So, minimum value is 37.5.

Therefore, the correct option is D.

3 0

3 years ago

A length of rope is stretched between the top edge of a building and a stake in the ground. The rope also touches a tree halfway

mestny [16]

the tree is 8 ft because it is half of the building

3 0

2 years ago

Alice is making a sandwich to pack in her lunch. She has 2 different kinds of bread, 3 cheeses, 4 lunch meats, and 2 condiments

Evgen [1.6K]

To find the number of possible sandwiches, all you have to do is multiply the numbers of different ingredients together:

2 x 3 x 4 x 2
= 6 x 8
= 48

She can make 48 different sandwiches. :)

5 0

3 years ago

There is a bag with only red marbles and blue marbles.

zaharov [31]

Answer: 56

Step-by-step explanation:

Given that :

Marbles in bag are only red and blue ;

Probability of randomly choosing a red = 2/7

Number of red marbles in bag = 16

The total Number of marbles =?

P(choosing a red marble) = required outcome / Total possible outcomes

Required outcome = number of red marbles

Total possible outcomes = total number of blue and red marbles

Total number of blue and red marbles = x

P(choosing a red marble) = required outcome / Total possible outcomes

2/7 = 16 / x

Cross multiply

2x = 16 * 7

2x = 112

x = 112 / 2

x = 56 marbles

Total number of marbles = 56

3 0

2 years ago

Find the x-intercepts and y-intercepts of 10x+6y=-4

NISA [10]

The x intercept is $(\frac{-2}{5}, 0)$

The y intercept is $(0, \frac{-2}{3})$

Solution:

Given equation is:

10x + 6y = -4

The x intercept is the point where the line crosses the x axis

The y intercept is the point where the line crosses the y axis

Find x intercept:

Substitute y = 0 in given equation

10x + 6(0) = -4

10x = -4

$x = \frac{-4}{10}\\\\x = \frac{-2}{5}$

Thus the x intercept is $(\frac{-2}{5}, 0)$

Find y intercept:

Substitute x = 0 in given equation

10(0) + 6y = -4

$6y = -4\\\\y = \frac{-4}{6}\\\\y = \frac{-2}{3}$

Thus the y intercept is $(0, \frac{-2}{3})$

6 0

3 years ago