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Arada [10]
3 years ago
7

Suppose that a factory manufactures only tables and chairs and that the profit on one chair is $15 and on the table is $20. Each

chair requires 1 large piece and 2 small pieces. Each table requires 2 large pieces and 2 small pieces (see Figure 1 below). Finally, suppose that you have only 6 large pieces and 8 small pieces. How many chairs and how many tables should you build to maximize profit? Write a system of equations using inequalities and constraints
Mathematics
1 answer:
Leya [2.2K]3 years ago
5 0

Answer:

The data we have is:

Profit per chair = $15

Profit per table = $20

Chair needs: 1 large pice, 2 small pieces.

Table needs: 2 large pieces, 2 small pieces.

You have 6 large pieces and 8 small pieces, and you want to maximize the profit.

Let's define:

T = # of tables

C = # of chairs.

Total profit:

P = C*$15 + M*$20

The number of chairs that you can make is given by:

0 ≤ C ≤ 4

If you make 4 chairs, the profit is:

P = 4*$15 = $60

And there will be 2 large pieces left.

Now for the tables.

0 ≤ T ≤ 3

If you make 4 tables, the profit will be:

P = 3*$20 = $60 (same as before)

And there will be two small pieces left.

Then we want to use a medium number of tables and chairs, we can not use the maximum for any of those, the first thing we should try is:

we ideally would want to use all the pieces that we have.

8 small, 6 large:

Then we can make:

2 tables: we use 4 large pieces and 4 small pieces.

T = 2

And we have left 2 large pieces and 4 small pieces.

The leftover is enough to make two chairs.

C = 2.

In this case, where we used all our materials, the profit will be:

P = 2*$15 + 2*$20 = $30 + $40 = $70

The profit is maximized when we make 2 tables and two chairs.

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There is one solution. The solution of the system is (9,-5)

Option A is correct.

Step-by-step explanation:

We need to solve the system of equations by elimination method

6x= 64+2y\\2x= -7-5y

Rearranging the equations:

6x-2y=64\,\,\,eq(1)\\2x+5y=-7\,\,\,eq(2)

Eliminating y to find value of x:

Multiply eq(1) by 5 and eq(2) by 2 and add both equations:

30x-10y=320\,\,\,\\4x+10y=-14\\--------\\34x=306\\x=\frac{306}{34}\\ x=9

So, value of x= 9

Eliminating x to find value of y:

Multiply eq(1) by 2 and eq(2) by 6 and subtract both equations:

12x-4y=128\\12x+30y=-42\\-\,\,\,\,-\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+\\---------\\-34y=170\\y=\frac{170}{-34}\\ y=-5

So, value of y = -5

There is one solution. The solution of the system is (9,-5)

Option A is correct.

Keywords: Solving system of equations

Learn more about Solving system of equations at:

  • brainly.com/question/13168205
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#learnwithBrainly

5 0
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Determine the number of gallons of gas that your car holds. Find the cost of the type of gasoline that your car uses at a local
Alex17521 [72]

16 gallon tank, 2.75 $/gal so roughly 53.25


3 0
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Sal the sloth takes one hour to travel 7 1/2 feet. If he continues to travel at the same rate, how long will it take him to trav
pentagon [3]

Answer:

4 hours

Step-by-step explanation:

Since we know he travels at a rate of 1:7.5 all we have to do is divide 7.5 by 30. Do you use proportions? You can set this up as a proportion and the find answer easily.

1\frac{1}{7.5} =\frac{x}{30}

Now we cross product.

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1x30=30

so now we have

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Now we have to divide 7.5 on both sides which gives us

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2 years ago
Which table represents the same linear relationship as y = x + 3?
Ilia_Sergeevich [38]

Answer:

The seconf option

x = 0, 2, 4

y = 3,5,7

Step-by-step explanation:

plug in your x and y points into the equation and they should be the same of both sides

ex (0,3)

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2 years ago
JEEEEEEEEEEEEEEEEEEELPPPPP
ololo11 [35]

Answer:

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Step-by-step explanation:

The formula for length of the circle is =

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Therefore

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Therefore the Arc length =37.68/2

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