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Given the linear programming problem, use the method of corners to determine where the minimum occurs and give the minimum value.Minimize

Exam Image

Subject to
x ≤ 3
y ≤ 9
x + y ≥ 9
x ≥ 0
y ≥ 0

Answers

Answer 1

Answer:

Answer:

Minimum value of function $C=x+10y$ is 63 occurs at point (3,6).

Step-by-step explanation:

To minimize :

$C=x+10y$

Subject to constraints:

$x\leq 3---(1)\ny\leq 9---(2)\nx+y\geq 9----(3)\nx\geq 0\ny\geq 0$

Eq (1) is in blue in figure attached and region satisfying (1) is on left of blue line

Eq (2) is in green in figure attached and region satisfying (2) is below the green line

Considering $x+y\geq 9$ , corresponding coordinates point to draw line are (0,9) and (9,0).

Eq (3) makes line in orange in figure attached and region satisfying (3) is above the orange line

Feasible region is in triangle ABC with common points A(0,9), B(3,9) and C(3,6)

Now calculate the value of function to be minimized at each of these points.

$C=x+10y$

at A(0,9)

$C=0+10(9)\nC=90$

at B(3,9)

$C=3+10(9)\nC=93$

at C(3,6)

$C=3+10(6)\nC=63$

Minimum value of function $C=x+10y$ is 63 occurs at point C (3,6).

Answer 2

Answer:

Applying the method of corners to the linear programming problem yields a minimum value of 6 at the point (3, 0) for the given objective function and constraints.

The linear programming problem involves minimizing an objective function subject to certain constraints. The constraints are given as follows:

Minimize z = 2x + 3y

Subject to:

x ≤ 3

y ≤ 9

x + y ≥ 9

x ≥ 0

y ≥ 0

To find the minimum value, we employ the method of corners. The feasible region is determined by the intersection of the inequalities. The corner points of this region are where the constraints intersect.

Intersection of x ≤ 3 and y ≥ 0 gives the point (3, 0).

Intersection of y ≤ 9 and x ≥ 0 gives the point (0, 9).

Intersection of x + y ≥ 9 and y ≥ 0 gives the point (9, 0).

Now, evaluate the objective function z = 2x + 3y at each corner point:

z1 = 2(3) + 3(0) = 6

z2 = 2(0) + 3(9) = 27

z3 = 2(9) + 3(0) = 18

The minimum value occurs at point (3, 0) with z_min = 6.

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15v - 17

Step-by-step explanation:

3+ – 5(4+ – 3v) can be written as

3 - 5( 4 - 3v)

Expand and simplify

That's

3 - 20 + 15v

15v - 17

Hope this helps you

Which method can be used to find the area of the composite shape? 2 semicircles on each side of a rectangle. Decompose the figure into one semicircle and one rectangle and add the areas. Decompose the figure into one semicircle and one rectangle and subtract the areas. Decompose the figure into two semicircles and one rectangle and subtract the areas. Decompose the figure into two semicircles and one rectangle and add the areas.

Answers

Answer:

Decompose the figure into two semicircles and one rectangle and add the areas.

Step-by-step explanation:

A composite shape is a given shape that comprises more than a plane figure. The total area is determined by addition of separate areas of figures making up the composite figure.

When two semicircles are included on the two sides of a rectangle, a composite figure is formed. To determine its area, calculate the individual areas of each semicircle and rectangle, then add the values.

Therefore, decompose the figure into two semicircles and one rectangle and add the areas is the accurate answer.

Answer:

The Answer is (D)

Step-by-step explanation:

Please help, i will give brainliest

Answers

Answer:

Step-by-step explanation:

hope i helped

Ethan buys 4 packs of muffins. He uses a Coupon and saves $2 off the total.Which expression represents his total cost?

A. 4+2

B. 4m -2

C. 4m + 2

D. 4 - 2m

Answers

This expression represents Ethan's Total cost after using the coupon cost after using the coupon would be:4m - 2

Ethan buys 4 packs of muffins. He uses a coupon and saves $2 off the total.

Let's find out which expression represents his total cost.

Step 1: Determine the cost of one pack of Muffins

To determine the cost of one pack of muffins, we need to use algebra.

Let m be the cost of one pack of muffins. If Ethan buys 4 packs of muffins, then his total cost before using the coupon would be 4m.

Step 2: Use the coupon to calculate the total Cost Now let's use the coupon to calculate Ethan's total cost.

We know that he saved $2 off the total.

Therefore, his total cost after using the coupon would be:4m - 2

This expression represents Ethan's total cost after using the coupon. Therefore, the correct answer is option B: 4m - 2.

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Is the opposite of an opposite number always going to be positive?

Answers

No, the opposite of an opposite will not always be positive. the opposite of -4 is 4, and the opposite of that is -4, so the opposite of the opposite of the number -4 is -4, which is not positive. On the other hand, it CAN be positive. The opposite of 7 is -7, and opposite of that is 7, which is positive.

yes it is because if you reflect for a min, the opposite (which is a negative) of the opposite is always going to be a positive.

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Given the linear programming problem, use the method of corners to determine where the minimum occurs and give the minimum value.MinimizeExam ImageSubject tox ≤ 3y ≤ 9x + y ≥ 9x ≥ 0y ≥ 0

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Given the linear programming problem, use the method of corners to determine where the minimum occurs and give the minimum value.Minimize

Exam Image

Subject to
x ≤ 3
y ≤ 9
x + y ≥ 9
x ≥ 0
y ≥ 0