Solve and graph the inequality on a number line: −19

Beth is knitting mittens and gloves. Each pair must be processed on three machines. Each pair of mittens requires 2 minutes on M

anygoal [31]

Answer:

Two mittens and seven gloves

Step-by-step explanation:

I presume you are asking how many mittens and how many gloves Beth should knit to produce the most profit.

Let x = the number of mittens and

Let y = the number of gloves

1. Summarize the information in a table

$\begin{array}{cccc}&\textbf{Mittens}& \textbf{ Gloves} & \textbf{Minutes Available}\\\text{Machine A} & 2 & 4 & 32\\\text{Machine B} & 2 & 2 & 18\\\text{Machine C} & 4 & 1 & 24\\\text{Unit profit} & $8.00 & $10.00 & \\\end{array}$

2. List the constraints

(a) Beth can't make a negative number of mittens, so

x ≥ 0.

(b) Neither can she make a negative number of gloves, so

y ≥ 0.

(c) The total number of minutes on Machine A cannot exceed 32, so

2x + 4y ≤ 32.

(d) The total number of minutes on Machine B cannot exceed 18, so

2x + 2y ≤ 18.

(e) The total number of minutes on Machine C cannot exceed 24, so

4x + y ≤ 24.

3. Write an equation for the profit

P = 8.00x + 10.00y

4. Graph the constraints to identify the feasible region

See the figure below. The feasible region is the dark green area where all three regions overlap.

5. Determine the points of intersection between the constraints

(i) Constraints (c) and (d)

$\begin{array}{rcr}2x + 4y & = & 32\\2x + 2y & = & 18\\2y & = & 14\\y & = & \mathbf{7}\\2x + 14 & = & 18\\2x & = &4\\x & = & \mathbf{2}\\\end{array}\\$

The lines intersect at (2,7).

(ii) Constraints (c) and (e)

$\begin{array}{rcl}2x + 4y & = & 32\\4x + y & = & 24\\4x + 8y & = & 64\\7y & = & 40\\y & = & \mathbf{\dfrac{40}{7}}\\\\4x + \dfrac{40}{7} & = & 24\\\\4x & = &24 - \dfrac{40}{7}\\\\4x & = & \dfrac{128}{7}\\\\x & = & \mathbf{\dfrac{32}{7}}\\\\\end{array}\\$

The lines intersect at (27/7,32/7).

(iii) Constraints (d) and (e)

$\begin{array}{rcr}2x + 2y & = & 18\\4x + y & = & 24\\4x + 4y & = & 36\\3y & = & 12\\y & = & \mathbf{4}\\4x +4 & = & 24\\4x & = &20\\x & = & \mathbf{5}\\\end{array}\\$

The lines intersect at (5,4).

6. Determine the x- and y-intercepts of the feasible region

(i) x-intercept

$\begin{array}{rcr}4x + y & = & 24\\4x + 0 & = & 24\\x & = & \mathbf{6}\\\end{array}$

The x-intercept is at (6,0).

(ii) y-intercept

$\begin{array}{rcr}2x + 4y & = &32\\2(0) + 4y & = &32\\4y & = & 32\\y & = & \mathbf{8}\\\end{array}$

The y-intercept is at (0,8).

The five black dots are the vertices of the polygon that represents the feasible region.

7. Calculate the maximum profit

Calculate the profit at each of the vertices.

(i) At (0,0)

P = 8.00x + 10.00y = 8.00(0) + 10.00(0) = 0 + 0 = $0

(ii) At (2,7)

P = 8.00(2) + 10.00(7) = 16 + 70 = $86

(iii) At (5,4)

P = 8.00(5) + 10.00(4) = 40 + 40 = $80

(iv) At (6,0)

P = 8.00(6) + 10.00(0) = 48 + 0 = $48

The maximum profit occurs at (2,7)

Thus, Beth should knit two mittens and seven gloves.

7 0

4 years ago

Y=3x-7 Y=3x+4 solving the special system of liner equations ?

DIA [1.3K]

Answer:

No Solution.

Step-by-step explanation:

y=3x-7

y=3x+4

-----------

3x-7=3x+4

3x-3x-7=4

-7=4

no solution.

4 0

3 years ago

Samantha is using a 2-liter pitcher to serve lemonade to 10 of her friends. How many times will she need to fill the pitcher in

Mice21 [21]

Answer: 2 times

Step-by-step explanation:

Hi, since 1000 milliliters = 1 liter

We have to convert the 2 liters into milliliters:

2 x 1000 = 2000 milliliters, so she is using a 2,000 milliliters pincher.

Now we have to multiply the number of friends (10) by the amount of lemonade she serves to each one (400 ml)

400 x 10 = 4,000 milliliters

Finally, we have to divide the amount of lemonade she needs to serve (4,000 ml) by the capacity of the pitcher (2,000), to obtain the number of times that she will need to fill the pitcher.

4,000/2,000=2 times

Feel free to ask for more if needed or if you did not understand something.

4 0

3 years ago

Read 2 more answers

Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the ta

Evgen [1.6K]

Answer:

1) He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

2) He did not multiply the numerator and denominator by the correct number to equal 1,500.

5) He should have multiplied the numerator and denominator by 75, not 30, because 20 x 75 = 1,500.

Step-by-step explanation: