Exercise 1 Usage of free production capacity
A factory has ended a non-profitable production line. As a result, there is a reasonable amount
of free production capacity available. The management team considers to use this capacity for
manufacturing one or more of the products A, B and C. Before a product can be sold it has to be
treated by 3 machines. The table below shows the available capacity per machine and the amount
of hours required to manufacture a product:
Machine type Available capacity Product A Product B Product C
(hours per week)
Machine 1
500
9
3
5
Machine 2
350
5
4
0
Machine 3
150
3
0
2
It is expected that each unit of product A and B that is manufactured can be sold, while the
number of sales of product C is at most 20 units per week. The profit per unit is 50, 20 and 25 Euro
for product A, B and C, respectively. The manufacturing team wants to maximize total profit.
Formulate this problem as a linear programming problem and explain which decision variables are
used.

Answer:

[tex]x = 4.8[/tex]

Step-by-step explanation:

[tex] \frac{3}{4} = \frac{3.6}{x} [/tex]

[tex]3x = 14.4[/tex]

[tex]x = 4.8[/tex]

Answer:

A circle.

Step-by-step explanation:

Ok, any plane has a vector normal to it.

Then the plane that cuts the sphere, has a normal vector.

If we draw that normal vector such that it passes through the center of the circle, we can think of this as the "axis" of a cylinder.

Such that when we step on any point of that vector, all the points of the spere that can be reached with a perpendicular line to the vector (like the radius in polar coordinates) are at the same distance of the vector.

Then we can conclude that when we cut a sphere with a plane, the cross-section will be always a circle.

Then the shape that is a representation of the cross-section is a circle.

Answer: You get to keep 1,673.24

You pay 272.38 in taxes.

Answer:

of the students who live more than one mile

away, about 76% ride a bike.

Step-by-step explanation:

Answer:

Use geogebra it is a helpful website that helps you plot points, and find where things go. The second one is c. y=25x.

Step-by-step explanation:

Answer:

72 miles

Step-by-step explanation:

To solve this problem, you can use the pythagorean theorem, which is a^2 + b^2 = c^2. We already have b equal to 54 miles, and since c is the hypotenuse, it equals 90 miles. We can substitute the values into the formula to get:

a^2 + 54^2 = 90^2

a^2 + 2916 = 8100

a^2 = 5184

a = 72 miles

Step-by-step explanation:

The parabola has a line of symmetry at x=0 so that means we can reflect the function across the y axis and it will remain unchanged so the answer is even function.

Let x be the amount invested at 10%;

SO we have;

.10x=amount invested at 10%

(4000-x).12=amount invested at 12%

So our equation would be;

.10x+(4000-x).12=460

Distribute the 12%;

.10x+480-.12x=460

Put like terms together so you can see them better;

.10x-.12x+480=460

-.02x+480=460;

subtract 480 from both sides;

-.02x=-20

Multiply each side by -.02;

x=1000

Now that we know what was invested at 10% we can subtract that from $4000 to get what was invested at 12%;

$4000-$1000=$3000

Hope you understand

=)

Answer: The width of the rectangle is 10.2 inches, the perimeter is 71.4 inches,  the area is 260.1 inches.

Step-by-step explanation:

25.5/5=5.1

5.1*2=10.2

The width is 10.2 inches

25.5*2+10.2*2=71.4

The perimeter is 71.4 inches

20.5*10.2=260.1

The area is 260.1

1) The width of the rectangle is 10.2 in.

2) The perimeter of the rectangle is 71.4 in.

3) The area of the rectangle is 260.1 sq.in.

[tex]P=2\times(l+w)[/tex]

where, 'l' is the length of the rectangle

'w' is the width of the rectangle

[tex]A=l\times w[/tex]

For given example,

The sides of a rectangle are in the ratio 2:5

The longer side of the rectangle is 25.5 in.

This means the length of the rectangle is [tex]l=25.5~in.[/tex]

Let 'x' represents the width of the rectangle.

⇒ [tex]\frac{2}{5} =\frac{x}{25.5}[/tex]

⇒ 2 × 25.5 = 5 × 'x'

⇒ 51 = 5x

⇒ x = 51/5

⇒ x = 10.2 in.

This means the width of the rectangle is 10.2 in.

⇒ [tex]l=25.5~in,~w=10.2~in.[/tex]

Using the formula of perimeter of the rectangle,

⇒ P = 2 × (25.5 + 10.2)

⇒ P = 2 × 35.7

⇒ P = 71.4 in.

Using the formula of area of the rectangle,

⇒ A = 10.2 × 25.5

⇒ A = 260.1 sq. in.

Therefore, the width of the rectangle is 10.2 in.

The perimeter of the rectangle is 71.4 in.

The area of the rectangle is 260.1 sq.in.

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Answer:

45/22

Step-by-step explanation:

Answer:

-3 and -8

Step-by-step explanation:

Let the two numbers be called a and b respectively. We can say that ab=-24, and a+b=-11.

If a+b=-11, a=-11-b.

ab=-24

(-11-b)b=-24

b²+11b+24=0

(b+3)(b+8)=0

b=-3, b=-8

a=-11-b=-11+3=-8

a=-11-b=-11+8=-3

So the numbers are -3 and -8

Answer:

6/5

Step-by-step explanation:

For this you need to clear the formula for the area which is bxh/2=A, now you need to clear the base and the formula would be b=Ax2/h, and would be (9/20)x2/ 3/4 equal to 18/20 / 3/4 and gives the result of 72/60,now you need to simplify and the simplest form is 6/5

The base of the triangle with area of 9 / 20 centimetres squared and height of 3 / 4 centimetres is 6 / 5 centimetres.

area of a triangle = 1 / 2 bh

where

Therefore,

area = 9 / 20 cm²

height = h = 3 / 4 cm

b = ?

Hence.

area of the triangle = 1 / 2 bh

9 / 20 = 1 / 2 × 3 / 4 × b

9 / 20 = 3 / 8 b

cross multiply

9 × 8 = 20 × 3b

72 = 60b

b = 72 / 60

b = 12 / 10 = 6 / 5

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Answer:

Grapes are less expensive

Step-by-step explanation:

First, find how much money 1 pound of each fruit is:

Bananas: $1.47 / 3 = $0.49

Grapes: $1.18 / 2 = $0.59

Compare:

0.49 < 0.59

So grapes are less expensive

Answer:

53 1/3 cups

Step-by-step explanation:

if there are 80 glasses and each glass has 2/3 of juice in it, there will be 53 1/3 cups in total because 80 x 2/3 = 53 1/3

Answer:

Surface area of figure = 200.52 meter²

Step-by-step explanation:

Given:

Side of square cut = 12 meter

Diameter of semi circle = 12 meter

Find:

Surface area of figure

Computation:

Diameter of semi circle = 12 meter

Radius of semi circle = Diameter of semi circle / 2

Radius of semi circle = 12 / 2

Radius of semi circle = 6 meter

Surface area of figure = Surface area of square + Surface of cylinder

Surface area of figure = [Side x Side] + πr²/2

Surface area of figure = [12 x 12] + (3.14)(6)²/2

Surface area of figure = [144] + (3.14)(36)/2

Surface area of figure = 144 + 56.52

Surface area of figure = 200.52 meter²

Answer:

Unless I'm misunderstanding it should be 100% or 1/1  because something that is 100% likely to happen will always happen.

Step-by-step explanation:

If there is anything else that may change my understanding of this please send it otherwise I hope this helps.

The value of P(A) is 1 where A is the event that is certain to occur because the probability of any event is 1 which means that event is certain to occur.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

If event A is certain to occur.

As we know,

From the definition of probability, the ratio of the number of favorable outcomes to the total number of outcomes

The value of the probability lies between 0 to 1 or [0, 1]

If the probability of any event is 0 that means that event cannot happen.

If the probability of any event is 1 that means that event is certain to occur.

Event A is certain to occure.

P(A) = 1

Thus, the value of P(A) is 1 where A is the event that is certain to occur because the probability of any event is 1 which means that event is certain to occur.

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Answer:

whats this? can you provide more context?

Step-by-step explanation:

Answer:

Ask you teachers if they can give you extra assignments for extra credit! Sometimes they will!

9514 1404 393Answer:

Step-by-step explanation:

Let c and w represent the per-picture cost of the class picture and a wallet-size picture, respectively. The two packages can be described by ...

  c +10w = 19

  2c +15w = 31

Subtracting the second equation from twice the first, we get ...

  2(c +10w) -(2c +15w) = 2(19) -31

  5w = 7

  w = 1.40

Substituting into the first equation, we can find the cost of a class picture.

  c + 10(1.40) = 19

  c = 5 . . . . . . . . . . . subtract 14

A class picture costs $5; a wallet-size picture costs $1.40.

Answer:

lateral area = 308 ft

surface area = 616 ft

Answer:

24p

Step-by-step explanation:

I'm pretty sure that this is the answer because the question was "What is the value P(24)?" which means you have to use the commutative property to reorder the terms.

Hope this helped!

Answer:

The answer is in the picture I couldn't type it sorry.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The freight charge on a shipment of 1200 kg is $84.00. So, the rate per 100 kg would be $7.00. option D is correct.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

It is given that the freight charge on a shipment of 1200 kg is $84.00. we need to find the rate per 100 kg.

So, by the unitary method,

The freight charge on a shipment of 1200 kg = $84.00.

The freight charge on a shipment of 1 kg = 84/ 1200

The freight charge on a shipment of 100 kg = 84/ 1200

                                                                           = 84 x 100/ 1200

                                                                            = $7.00

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Answer:

5.5

Step-by-step explanation:

Answer:

5.5

Step-by-step explanation:

multiply the length value by 5.5

You want math problems???

Answer:

Hᴇʏᴀᴀᴀ!! ᴍʏ ɴᴀᴍᴇ ɪꜱ ᴘɪɴᴋʏ ᴀɴᴅ ɪ ᴀᴍ ʜᴇʀᴇ ᴛᴏ ᴀɴꜱᴡᴇʀ ʏᴏᴜʀ Qᴜᴇꜱᴛɪᴏɴ!!ʕ ꈍᴥꈍʔ☆

Step-by-step explanation:

ɪ ᴅᴏɴ'ᴛ ʀᴇᴀʟʟʏ ʟɪᴋᴇ ᴍᴀᴛʜ ʙᴜᴛ ɪꜰ ɪ ʜᴀᴅ ᴛᴏ ᴄʜᴏᴏꜱᴇ ᴀ ꜰᴀᴠᴏʀɪᴛᴇ ɪᴛ ᴡᴏᴜʟᴅ ʙᴇ ᴀʟɢᴇʙʀᴀ!!  (◕ᴗ◕✿)

  ʜᴀᴠᴇ ᴀɴ ᴀᴍᴀᴢɪɴɢ ɴɪɢʜᴛ ᴏʀ ᴅᴀʏ!

      *:･ﾟ✧*:･ﾟꜰʀᴏᴍ ʏᴏᴜʀ ᴏɴᴇ ᴀɴᴅ ᴏɴʟʏ ᴘɪɴᴋʏ  ʕ ﾟ ● ﾟʔ✧✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ

Answer: A

Step-by-step explanation:

Answer:

the buttons are alredy on the calculator.

Step-by-step explanation:

Answer:

too difficult 99%(95%) fraction and decimal of 26.5 and (-36)

Answer:1320

Step-by-step explanation:Only one person can win first, second and third place. The total number of placers is 12 times 11 times 10.

Answer:

Usig their skills by:

Step-by-step explanation:

Using their strengh, force, move your feet, and arms with strong force to push you ahead faster and faster, if u are really tired I would keep going,