What is the area of the figure?

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

3 years ago

a muffin recipe calls for 2 cups of flour and 3 oz of milk. if the recipe is increased to use 9 cups of flour , how much milk is

Tasya [4]

Answer:13.5 oz of milk

Step-by-step explanation:

2/3=9/x

Cross product

2×x=9×3

2x=27

X=27/2

X=13.5

5 0

3 years ago

Help!

alexira [117]

Answer:

410 student and 436 adult tickets

Step-by-step explanation:

x is the number of student tickets and y is the number of adult tickets sold. we now that a total of 846 tickets were sold so x+y=846=>x=846-y. we also now that their worth was 3 846usd so 3*x+6*y=3846. we substitute x and are left with the following equation:3x+6*(846-x)=3846

5076-3x=3846

3x=1230

x=410

=>y=846-410=436

4 0

3 years ago

Please see attached pic

BigorU [14]

Answer:

D is the correct answer.

Step-by-step explanation:

-Subtract final value by start value

-Divide by start value

-Multiply by 100

6 0

3 years ago

Read 2 more answers

A company needs to package 2,400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container

Agata [3.3K]

If the company used rectangular prisms it would take 40 boxes (2400/60) to hold 2,400 pencils which would cost $20 (40 times 0.50). If they used cylindrical containers, they would need 30 containers (2400/80) for a total of $22.50 (30*0.75).

To minimize the cost the company should go with rectangular prisms as they are the most cost effective.

6 0

3 years ago