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katrin [286]
3 years ago
8

A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of m

achines A, B, and C. Each machine A costs $80,000 and requires 2,000 square feet of floor space. Each machine B costs $50,000 and requires 3,000 square feet of floor space. Each machine C costs $40,000 and requires 5,000 square feet of floor space. The machines can produce 200, 250 and 350 units per day respectively. The plant can only afford $500,000 for all the machines and has at most 20,000 square feet of room for the machines. The company wants to buy as many machines as possible to maximize daily production.
Let Xi = number of machines of type i purchased

MAX: 200X1 + 250X2 + 300X3

Subject to: 2X1 + 3X2 + 5X3 ≤ 20

80X1 + 50X2 + 40X3 ≤ 500

X1, X2, X3 ≥ 0

A

B

C

D

E

F

1

Capital Expansion

2

3

Machine Types

4

Machine 1

Machine 2

Machine 3

5

Number to buy

Total Output:

6

Machine output

200

250

350

7

8

Requirements:

Used

Available

9

Square feet

2,000

3,000

4,000

20,000

10

Cost

80,000

50,000

40,000

500,000

How many of each machine should they purchase?
Mathematics
1 answer:
katovenus [111]3 years ago
3 0

Answer:657

Step-by-step explanation:

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So, Option (D) is your answer! Hope this helps!!
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3 years ago
Jenna+has+five+less+stamps+than+horacio.+gary+has+half+the+number+that+horacio+had.+all+together+they+have+a+total+of+75+stamps
nexus9112 [7]
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4 0
2 years ago
this rectangular prism is cut by the plane shown. The plane is perpendicular to the base of the rectangular prism. What is the s
Musya8 [376]

Answer: REACTANGLE !!!!!!!!!!!

Step-by-step explanation:

The shape of the cross-section is a rectangle. The plane is perpendicular to the base of the rectangular prism so the shape of the cross-section is the same as the top and bottom views of the rectangular prism.

4 0
2 years ago
Read 2 more answers
Find the intervals on which​ f(x) is​ increasing, the intervals on which​ f(x) is​ decreasing, and the local extrema. f (x )equa
Kaylis [27]

Answer:

f(x) is increasing in the intervals (-∞,-4) and (9,∞)

f(x) is decreasing in the ingercal (-4,9)

The local extrema is:

local max at (-4,496)

and local min at (9,-1701)

Step-by-step explanation:

In order to solve this problem we must start by finding the derivative of the provided function, which we can find by using the power rule.

if f(x)=ax^{n} then f'(x)=anx^{n-1}

so we get:

f(x)=2x^{3}-15x^{2}-216x

f'(x)=6x^{2}-30x-216

in order to find the critical points we mus set the derivative equal to zero, since the local max an min will happen when the slope of the tangent line to the given point is zero, so we get:

6x^{2}-30x-216=0

we can solve this by factoring, so let's factor that equation:

6(x+4)(x-9)=0

we can now set each of the factors equal to zero so we get:

x+4=0 and x-9=0

when solving each for x we get that:

x=-4 and x=9

These are our critical points, now we can build the possible intervals we are going to use to determine where the function will be increasing and where it will be decreasing:

(-∞,-4), (-4,9) and (9,∞)

so now we need to test these intervals in the derivative to see if the graph will be increasing or decreasing in the given intervals. So let's pick x=-5 for the first one, x=0 for the second one and x=10 for the third one.

When evaluating them into the first derivative we get that:

f'(-5)=84, this is a positive answer so it means that the function is increasing in the interval (-∞,--4)

f'(0)=-216, this is a negative anser so it means that the function is decreasing in the interval (-4,9)

f'(10)=84, this is a positive answer so it means that the function is increasing in the interval (9,∞)

Now, for the local extrema, we can see that at x=-4, the function it's increasing on the left of this point while it's decreasing to the right, which means that there will be a local maximum at x=-4, so the local max is the point (-4,496)

We can see that at x=9, the function it's decreasing on the left of this point while it's increasing to the right, which means that there will be a local minimum at x=-9, so the local min is the point (9,-1701)

7 0
3 years ago
How many solutions are there to the equation below 9x + 27 = 9( x + 2 ) + 9
Nataly [62]

Let's solve the equation:

9x+27 = 9(x+2)+9 ← Distribute 9 to the x and 2

9x+27 = 9x+18+9 ← Combine like terms

9x+27 = 9x + 27 ← Subtract 27 from both sides

9x = 9x


Infinitely many solutions would be correct because no matter what x is, it will always equal each other the both sides of the equation because it is 9 times x on both sides.


7 0
2 years ago
Read 2 more answers
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