MATHEMATICS HIGH SCHOOL

In Andrew’s Furniture Shop, he assembles both bookcases and TV stands. Each type of furniture takes him about the same time to assemble. He figures he has time to make at most 18 pieces of furniture by this Saturday. The materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00. He has $600.00 to spend on materials. Andrew makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand. Find how many of each piece of furniture Andrew should make so that he maximizes his profit.

Answers

Answer 1
Answer:

Answer:

  • 6 bookcases
  • 12 TV stands

Step-by-step explanation:

Given Andrew has $600 for materials and can make 18 pieces of furniture, you want to know the number of each kind that maximizes profit if each bookcase costs $20 and gives $60 profit, while each TV stand costs $40 and gives $100 profit.

Setup

If x and y represent the numbers of bookcases and TV stands Andrew builds, respectively, then he wants to ...

  maximize 60x +100y

  subject to ...

  • x + y ≤ 18
  • 20x +40y ≤ 600

Solution

The attached graph shows the solution space for these constraints. The profit is maximized at the vertex of the space where the profit function line is farthest from the origin. Andrew maximizes his profit by building ...

  • 6 bookcases
  • 12 TV stands
Answer 2
Answer:

Final answer:

Andrew needs to solve a linear programming problem to find how many bookcases and TV stands he should manufacture for optimal profit. This is done by setting up and solving inequalities representing Andrew's time and material cost constraints, graphing the feasible region, and finding the point(s) in this region that yield the highest profit.

Explanation:

This question deals with the topics of linear programming and profit maximisation. Here, Andrew has to decide how much of each type of furniture, bookcases or TV stands, he should produce to maximise profit while considering time and material cost constraints.

From the given conditions, we get two inequalities. The first related to time says that the total number of bookcases and TV stands is less than or equal to 18: let bookcases be x, TV stands be y, thus we have x + y <= 18. The second involving the cost of material says that the total cost spent on materials for both products does not exceed $600: thus, we also have 20x + 40y <= 600.

You can graph these inequalities on the x-y plane to get a visual representation of the possibilities.

Finally, to find the optimal solution (i.e., the highest profit), you calculate the profit function P = 60x + 100y for each point in the feasible region and select the point that provides the highest profit.

Learn more about Linear Programming here:

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A painter worked 142 days last year. His total earnings for that time was $13,916. His approximate daily wage was___​

Answers

$98! Divide 1316/142

Answer:

His wage was 98 dollars per day.

Step-by-step explanation:

13,916÷142=98

98×142=13,916

Find the lateral area of a regular pentagonal pyramid that has a slant height of 14 in. and a base side length of 6 in. A) 210 in^2 B) 240 in^2 C) 42 in^2 D) 420 in^2

Answers

The question ask to choose among the following choices that contains the value of the lateral area of a regular pentagonal pyramid that has a slant height of 14 in and a base side length of 6 in. Base on my calculation, the answer would be A. 210 inch^2. I hope this would help 

The lateral area of a regular pentagonal pyramid has a slant height of 14 in is 210 inch^2.

We have given that ,

The lateral area of a regular pentagonal pyramid that has a slant height of 14 in. and a base side length of 6 in.

What is the pentagonal pyramid?

A pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point. Like any pyramid, it is self-dual. The regular pentagonal pyramid has a base that is a regular pentagon and lateral faces that are equilateral triangles.

The question ask to choose among the following choices that contain the value of the lateral area of a regular pentagonal pyramid that has a slant height of 14 in and a base side length of 6 in.

Base on my calculation, the answer would be A.

210 inch^2.

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Yoshi carries a balance on her credit card each month. In May, she decides she wants to use her card to buy a new dishwasher. In which part of the billing cycles charges to the minimum?

Answers

Answer:

When you do not have any past due

Step-by-step explanation:

For a minimum due, monthly payment your credit card company is willing to accept to not mark your account as “past due”. If Yoshi is paying every amount before the due date then she will be charged the least but anywhere in the cycle if the amount is paid beyond the due date, a hefty extra money will be paid.

The two box-and-whisker plots below show the scores on a math exam for two classes. What do the interquartile ranges tell you about the two classes?

Answers

The interquartile range is a measure that indicates the extent to which the central 50% of values within the data set are dispersed.
The interquartile range: Upper quartile - Lower quartile
As we can see in the box-and-whisker plots:
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Class B: 94-79 = 15
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Solve y = ax^2 + c for x.

Answers

The Value of x=±\sqrt{ (y-c)/(a)

To find the value of X.

What is Quadratic equation?

Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Assuming

a≠0...

First subtract c from both sides to get:

y-c=ax^(2)

Divide both sides by a and transpose to get:

x^(2) =(y-c)/(a)

So x must be a square root of (y-c)/(a) and we can deduce:

x=± \sqrt{(y-c)/(a)

So, the Value of x=±\sqrt (y-c)/(a)

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Answer:

b

Step-by-step explanation:

∆STV ~ ∆PQR. Find m∠P.129


9


86


6

Answers

Answer: 86^(\circ)

Step-by-step explanation:

Given :\triangle{STV}\sim\triangle{PQR}

We know that the corresponding angles of two similar triangles are congruent.

i.e. \angle{S}\cong\angle{P}                  (1)

\angle{T}\cong\angle{Q}

\angle{V}\cong\angle{R}

From the given picture , we have \angle{S}=86^(\circ)

Then from (1), \angle{P}=86^(\circ)

Hence, \angle{P}=86^(\circ)

m < P = m < S becuase the triangles are similar.

m < P = 86 degrees
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