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natta225 [31]
3 years ago
5

In Andrew’s Furniture Shop, he builds bookshelves and tables. Each type of furniture takes him about the same time to make. He f

igures he has time to make, at most, 25 pieces of furniture by this Saturday. The materials for each bookshelf cost him $20.00 and the materials for each table cost him $45.00. He has $675.00 to spend on materials. Andrew makes a profit of $60.00 on each bookshelf and a profit of $100.00 for each table. How many of each piece of furniture should Andrew make to maximize profit? A. define variables B. Write the constraint inequalities that represent the situation, and explain what each of the inequalities represents. (You should have four inequalities.) C. What are the vertices of the feasible region?
Mathematics
1 answer:
Paul [167]3 years ago
8 0
A. You may set the variables in either order. But for argument sake, let's set as follows:

x = Amount of bookshelves
y = Amount of tables

B. Because of the amount of things you need to make, the following is an inequality using those variables.

x + y > 25

Plus you can determine a second inequality based on the amount of money that you have to spend. 

20x + 45y < 675

Finally you may also add in that each value must be greater than or equal to zero, since they cannot have negative tables. 

C. By solving the system and looking at basic constraints when graphed, you can see the feasible region has 4 vertices. 

(0,0)
(18, 7)
(0, 15)
(33.75, 0) or (33, 0) if you insist on rounding. 
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pochemuha

Answer:

  263.08 m²

Step-by-step explanation:

The fraction of circle area that a sector represents is proportional to the central angle.

<h3>Proportion</h3>

  circle area/circle angle = sector area/sector angle

  circle area / 360° = 85.5 m² / 117°

Multiplying by 360°, we have ...

  circle area = (360/117)(85.5 m²) = 263.08 m²

The area of the circle is about 263.08 m².

6 0
1 year ago
This is a proportion. What is the value of X?
Verizon [17]

Answer:

x = 15 or x = - \frac{2}{5}

Step-by-step explanation:

Cross- multiplying gives

(14x + 6)(17x + 5) = 9x(27x + 11) ( expanding factors )

238x² + 172x + 30 = 243x² + 99x

rearrange into standard form : ax² + bx + c = 0

5x² - 73x - 30 = 0 ← in standard form

consider the factors of the product 5 × - 30 = - 150 which sum to the coefficient of the x-term (- 73 )

the factors are - 75 and + 2

Use these factors to split the middle term

5x² - 75x + 2x - 30 = 0 ( factor by grouping )

5x(x - 15) + 2(x - 15) = 0 ← take out the factor (x - 15)

(x - 15)(5x + 2) = 0

equate each factor to zero and solve for x

x - 15 = 0 ⇒ x = 15

5x + 2 = 0 ⇒ x = - \frac{2}{5}


7 0
2 years ago
?????????????????????
Paul [167]

Answer:

5x^2 + 7x

option C is your answer

6 0
3 years ago
Find the probability of each event. Write each answer as a fraction in simplest form, as a decimal to the nearest hundredth, and
Delvig [45]
Fraction: 1/2
decimal: 0.5
percent: 50%
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4 0
2 years ago
3(x-5)-15=48 how would this be solved?
natita [175]
<span>Problem: 3(x-5)-15=48

1. Multiply what's in the parenthesis
3x-15-15=48

2. Combine like terms
3x-30=48

3. Switch the sides
3x=48+30
3x=78

4. Divide

x=26

Answer: 26

</span><span>
</span>
5 0
2 years ago
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