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Leno4ka [110]
3 years ago
10

A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each chair ut

ilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed.
a. Write a mathematical model representing the store's constraints.
b. Suppose the profit on sofas is $200 and on chairs is $100. On a given day, the probability that a displayed sofa will be sold is 0.03 and that a displayed chair will be sold is 0.05. Mathematically model each of the following objectives:

1. Maximize the total pieces of furniture displayed.
2. Maximize the total expected number of daily sales.
3. Maximize the total expected daily profit.
Mathematics
1 answer:
miskamm [114]3 years ago
6 0

Answer:

a) 50S + 30C ≤ 800

b) 1) MAX = S + C

   2) Max = 0.03S + 0.05C

   3) Max = 6S + 5C

Step-by-step explanation:

Given:

Total space = 800 square feet

Each sofa = 50 square feet

Each chair = 30 square feet

At least 5 sofas and 5 chairs are to be displayed.

a) Write a mathematical model representing the store's constraints:

Let S denote number of sofas displayed and C denote number of chairs displayed.

The mathematical model will be:

50S + 30C ≤ 800

At least 5 sofas are to be dispayed: S ≥ 5

At least 5 chairs are to be displayed: C ≥ 5

b)

1) Maximize the total pieces of furniture displayed:

S + C = MAX

2) Maximize the total expected number of daily sales:

MAX = 0.03S + 0.05C

3) Maximize the total expected daily profit:

Given:

Profit on sofas = $200

Profit on chairs = $100

Max Expected daily profit =

Max = (200S * 0.03) + (100C * 0.05)

<em>Max = 6S + 5C</em>

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Answer:

A. add the areas of both bases to the rectangular area around the cylinder.

Step-by-step explanation:

If we flatten out the cylinder we would have two circles and a rectangle. When you roll up the rectangle, it would make the body of the cylinder. Surface area by definition the total area the surface of an object occupies.

So to get it, we add up the different shapes that make up the cylinder, which is the two circles and the rolled up rectangle.

7 0
3 years ago
How to solve all of this
photoshop1234 [79]
Start circle: πd = (3.14)(19) = 59.7

Move diagonally to the circle with the radius of 6.2.

Second circle: 2πr = 2(3.14)(6.2) = 39

Move upwards to the circle with the radius of 10.5

third circle: 2πr = 2(3.14)(10.5) = 66

Move right to the circle with the diameter of 16.6

Fourth circle: πd = (3.14)(16.6) = 52.2

Move down to the circle with the diameter of 7.7

fifth circle: πd = (3.14)(7.7) = 24.2

Move down to the circle with the diameter of 50

Sixth circle: πd = (3.14)(50) = 157.1

Move left to the circle with the radius of 11.8

Seventh circle: 2πr = 2(3.14)(11.8) = 74.1

Move down to the circle with the radius of 38

Eight circle: 2πr = 2(3.14)(38) = 238.8

Move right to the circle with the diameter of 1.1

ninth circle: πd = (3.14)(1.1) = 3.5

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Hope this helps :) 
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3 years ago
Write the decimal 1,072.039 in words
Rina8888 [55]
One thousand seventy two point thirty nine thousandths.

3 0
3 years ago
21.) A rectangle has an area of 36 square units. As the length and width change, what do you know about their
natima [27]

Answer:

the length and the width are inversely proportional to each other (l=\frac{36}{w} or w=\frac{36}{l})

Step-by-step explanation:

Let

l units = length of the rectangle,

w units = width of the rectangle.

The area of the rectangle is

\text{Area}=\text{Length}\cdot \text{Width}

A rectangle has an area of 36 square units, so

l\cdot w=36

Complete the table with some values of l and w that fit the previous formula:

\begin{array}{ccc}\text{Length}&\text{Width}&\text{Area}\\ \\36&1&36\cdot 1=36\ un^2.\\18&2&18\cdot 2=36 \ un^2.\\12&3&12\cdot 3=36\ un^2.\\ 9&4&9\cdot 4=36\ un^2.\\l&w&l\cdot w=36 \ un^2.\end{array}

As you can see, the length and the width are inversely proportional to each other (l=\frac{36}{w} or w=\frac{36}{l})

4 0
3 years ago
Math please help :)!!!
77julia77 [94]

Answer:

36, 8.5

Step-by-step explanation:

an exponent of two means that you are multiply a number by itself

so in this case you would multiply 6 by itself: 6 x 6

this gets you 36

and 8.5 doesn't change so its just 8.5

7 0
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