A store sells two types of toys, A and B. One unit of toys A yields a profit of $2, while a unit of toys B yields a profit of $3. The store owner, Anthony, estimates that no more than 2000 toys will be sold every month. Anthony pays $8 and $14 for each one of toy A and B respectively. He also does not plan to invest more that $25,000 in inventory of these toys. Identify the constraints that represent the situation.

Answers

Answer 1

Let x be the total number of toys A and y the number of toys B; x and y cannot be negative, hence
x≥0 and y≥0
The store owner estimates that no more than 2000 toys will be old every month.
x+y≤2000
One unit of toys A yields a profit of $2 while a unit of toys B yields a profit of $3, hence the total profit P is given by
P=2x+3y
The store owner pays $8 and $14 for each one unit of toy A and B respectively and he does not plant to invest more than $20,000 in inventory of these toys
8x+14y≤20,00
What do we have to solve?
Find x and y so that P=2x+3y is maximum under the conditions
x≥0
x≥0
x+y≤2000
8x+14y≤20,000

The solution set of the system of inequalities given above and the vertices of the region obtained are shown below:
Vertices of the solution set
A at (0,0)
B at (0.1429)
C at (1333,667)
D at (2000,0)
Calculate the total profit P at each vertex
P(A)=2(0)+3(0)=0
P(B)=2(0)+3(1429)=4287
P(C)=2(1333)+3(667)=4667
P(D)=2(2000)+3(0)=4000
The maximum profit is at vertex C with x=1333 and y=667
Hence the store owner has to have 1333 toys of type A and 667 toys of type B in order to maximize his profit

Related Questions

PLEASE HELP ME!!
SO HARD

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Answer:

0.5

Step-by-step explanation:

4m⁻³n⁻⁵ when m is 2 and n is 1

→ Rewrite with values substituted in

4 × ( 2 )⁻³ × ( 1 ) ⁻⁵

→ Evaluate

0.5

if i ate 2 dogs and started
off with 3 how many would i have?

Answers

Answer: 1

Step-by-step explanation:

you would be left with 1 dog because 3 minus 2 is 1.

Which graph represents the function of f(x) =
9x2 – 36/3x + 6?

Answers

12
(
2
x
−
1
)
x
i don’t have internet internet anymore but i don’t have internet internet so i don’t have internet internet so i

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Answers

Answer:

[tex] {3}^{3} \\ {g}^{5 } \\ a \\ {y}^{ - 2} \\ 1[/tex]

Two golf balls are randomly selected from a bag that contains 3 Titlist, 5 Top Flite, and 2 Pinnacle golf balls.
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Answers

Answer:

4.329

Step-by-step explanation:

Answer:2.329
Step by step

find the equation of the line shown

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Answer:

So Y always the double of x if x is 1 then y is 2 if x is 5 then y is 10 so the equation y=2x

Y= 2x

-9x²-11 = -452 solve to the nearest hundredth

Answers

Answer:

X = 7

Step-by-step explanation:

-9x^2 -11 = -452

+11 +11

____________

-9x^2 = -441

÷(-9) /÷ (-9)

____________

x^2 = 49

Square root for both

X = 7

Help stuck on this question

Answers

Answer:

< b = 73°

Step-by-step explanation:

The angle with a measure of < 73° has the same measure as < b because they are vertical angles. Two angles are vertical angles if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent.

Therefore, the correct answer is: < b = 73°

Một cột đèn cao 7m có bóng trên mặt đất dài 4 m. Hãy tính góc (làm tròn đến phút) mà tia sáng mặt trời tạo với mặt đất

Answers

Answer:

tg a = 7/4 => a ≈ 60°15'. chúc bạn thành công.

4m+2n=5n (solve for m)

Answers

M = 3n/4

Give me 5 stars if it helps

Answer:

m=3n/4

Step-by-step explanation:

4m+2n=5n subtract 2n from both sides

4m= 5n-2n combine like terms

4m=3n divide by 4

m=3n/4

brainliest plz <3

−0.18÷0.03 Write your answer in simplest form.

Answers

Answer:

-0.6

Step-by-step explanation:

Answer:

you just need to divide the two if I'm not missing anything -6

Step-by-step explanation:

-.18/.03 is -6

- 6x < 24
solve for x and what’s the solution?

Answers

Answer:

x > -4

Step-by-step explanation:

In order to get x by itself, you divide -6 on both sides. So, -6x divided by -6 = x and 24 divided by -6 equals -4.

However, the answer is not x < -4 because a rule of inequalities states that any time you divide or multiply both sides of an inequality by a negative number, the inequality sign is flipped. So, the answer is x > -4

Answer:

x > -4

Step-by-step explanation:

- 6x < 24

Divide each side by -6, remembering to flip the inequality

-6x/-6 > 24/-6

x > -4

Identify the transversal and classify the angle pair:

Answers

Answer:line l is the transversal because it intersect both sets of angles. and 7 and 11 are corresponding because they are in the same positions of the intersections.

Step-by-step explanation: usually a transversal is associated with parallel lines and corresponding angles are equal but this is not true with a triangle

please help! circled numbers only. tysm, will mark brainliest.

Answers

2. 1/5=3/15
4. 3/5=6/10
6. 8/9=32/36
8. 2/9=36/162
10. 5/12=30/72
12. 6/17=18/51
14. 9/15=3/5
16. 32/48=2/3
18. 54/72=3/4
20. n=4
22. n=32

Answer:

Please mark as BRAINLIEST

Step-by-step explanation:

2) 1/5 = 3/15

4) 3/5 = 6/10

6) 8/9 = 32/36

8) 2/9 = 36/162

10) 5/12 = 30/72

12) 6/17 = 18/51

14) 9/15 = 3/5

16) 32/48 = 2/3

18) 54/72 = 3/4

20) 20/45 = 4/9

22) 3/4 = 24/32

Factor the expressions
Please help

Answers

Answer:

[tex](x + 1)( {6x }^{2} - 2x)[/tex]

(X+1)(6x^2-2x)
2x(x+1)(3x-1)

Find the length of the third side. If necessary, round to the nearest tenth.
14
21

Answers

15.7

Step-by-step explanation:

rate as BRAINLIEST

[tex]a {}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {a }^{2} + {(14)}^{2} = {(21)}^{2} [/tex]

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7minutes for 3 songs =? Minutes for 6 songs

Answers

Step-by-step explanation:

7 minutes for 3 songs means for 6 songs it will take double the time since 6 is double of 3.

so 14 minutes for 6 songs

point to a parallel line (8,-8); 9x - 4y= 7

Answers

Answer:

y = 9/4x - 26

Step-by-step explanation:

9x - 4y= 7

-4y = -9x + 7

y = 9/4x - 7/3

y = 9/4x + b

-8 = 9/4(8) + b

-8 = 18 + b

-26 = b

Caravans use camels and wagons to travel on the Silk Road. Your caravan consists of 6 wagons. That's 1 more than c the number of camels. Write and solve an equation to find c

Answers

Answer:

5=c

Step-by-step explanation:

c= number of camels

6-1=c

5=c

The diameter of a circle is 2 centimeters. What is the area?
d=2 cm

Answers

Answer: 4π cm or 12.56 cm

Step-by-step explanation: To find the circumference of this circle, start with the formula for the circumference of a circle which is C = 2πr.

Since the radius is 2 centimeters, we can

plug in 2 centimeters for r in the formula.

So we have (2)(π)(2 cm) which is equal to 4π cm.

So the circumference of this circle is 4π cm.

Remember that π is approximately equal to 22/7 or 3.14 so we can estimate the value of the circumference by plugging in 3.14 for π.

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So the circumference of the circle is

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11.63 - 6.7 I need the answer.

Answers

Answer:

5.56. I think that is the answer

Answer: 4.93

Step-by-step explanation:

Its mental math

If A(1/3.5, 5) and B(10,39)..
Find the slope

Answers

Answer:

b 1/3.5

Step-by-step explanation:

How long would an airplane flying non-stop at 250km per hour take to fly 1 million kilometers? Give your answer in days and hours.

Answers

Answer:

166 days 4000 hours

Step-by-step explanation:

A website offers digital movie rentals for $2.95 per movie or a monthly subscription with unlimited movies for $12.95 per month. If Zara is a monthly subscriber, what is the minimum number of movies she must watch each month to save money compared to renting each movie separately?

Answers

Step-by-step explanation:

it would be merely 40%( rounding off)

The value of Hector's house has increased by 5%.
His house is now valued at £609 000
Work out the value of the house before the increase.

Answers

Answer:

$580000

Step-by-step explanation:

To find decrease we simply reverse the operations of increase

increase is x x 1.05 = 609000

x = 609000 / 1.05 = 580000 initial value

x= $580000

proof

580000 x 1.05 = 609000 new value

Please help me solve this please

Answers

hope this can help !!! :)

Nelson went grocery shopping. He spent $199.89. If the sales tax is 3.5%, what is the amount of tax that Nelson must pay?

Answers

3.5% of 199.89 is 6.99615, so the amount of tax that Nelson has to pay is $6.99615. Though we can round the thousandths place for the cost to be $7.

A box has a length of 30 inches, a width of 40 inches, and a height of 120 inches. Can a cylindrical rod with a length of 342.9 centimeters fit in the box?

Answers

Answer: 6 inches = 15.24 cm length

8 inches = 20.32 cm width

24 inches = 60.96 cm height

The diagonal along the side of the box = 20.32^2 + 60.96^2 = 4,129.024

square root (4,129.024) = 64.257 so the rod will fit diagonally.

Step-by-step explanation:

Find the missing side of each triangle. Leave your answer in simplest radical form.
(Please show ur work)

Answers

Answer:

Step-by-step explanation:

a²+b²=c²

10²+12²=c²

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[tex]\sqrt{244} =\sqrt{c^2} \\\sqrt{4} \sqrt{61}=c\\2\sqrt{61}=c[/tex]

>> Answer

_______

[tex] \: [/tex]

x² = 12² + 10²

x² = 144 + 100

x² = 244

x = √244

x ≈ 2√61m

Answer number 10 please thank you

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Answer:

125 blocks

Step-by-step explanation:

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