REALLY IN NEED OF HELP!! please do the best you can<3 Many companies make products to sell, either to other businesses or directly to consumers. The amount of money that a company collects from sales of its products is called its revenue. When a business produces a product, there are costs associated with production. For example, if a cola company is producing a diet cola, they incur costs from purchasing ingredients, aluminum to make cans, cardboard to make boxes, as well as the cost of paying their employees, and more. The profit that a company earns is the difference between the amount earned and the amount spent. Consider the lip color product from each of the two competing high-end cosmetic companies described below. The Alcone Company Besame Beauty This company makes a popular shade of lip color that retails for $45 per tube. The lip color costs The Alcone Company $36 per tube to make and the monthly costs associated with manufacturing just this color are $1,500. A popular shade of lip color from this company costs the consumer $55 per tube. The process to make the lip color costs Besame Beauty $44 per tube and the monthly costs associated with this are $2,200. Use the information given to explore some of the mathematical concepts you have practiced so far by answering the questions below. 1. Develop a single formula you can use to find the profit earned by both The Alcone Company and Besame Beauty for their lip color. Explain why your formula will work for both companies. 2. Write an expression that each company can use to describe the amount of money they will earn from selling their lip colors. Let x represent the number of tubes of lip color each company sells. 3. Write an expression that each company can use to describe the amount of money it costs them to manufacture the lip color each month. Let x represent the number of tubes of lip color each company sells. 4. Use your responses to questions 1, 2, and 3 to write fully simplified expressions each business could use to find their monthly profit. State which property of algebra you are using at each step. Remember that x represents the number of tubes of lip color each company sells. 5. If each company makes 225 tubes of their lip color this month, what amount of profit can they expect? Interpret your answers in terms of the problem’s context. 6. If each company makes and sells 150 tubes of their lip color this month, what amount of profit can they expect? Interpret your answers in terms of the problem’s context. 7. Explain how you used the order of operations to help you answer questions 5 and 6. 8. Explain how you figure out the number of tubes of lip color each company would need to manufacture and sell in order to earn a profit that is greater than 0. 9. Implement your plan from question 8. What is the minimum number of lip color tubes each company would need to manufacture and sell in order to earn a profit that is greater than 0? Interpret your answers in context of the question

Answer:

1. Profit =  Revenue - Cost

2.  For the Alcone Company Revenue = $45 × x

For the Besame Beauty Revenue = $55 × x

3.  Alcone Company; Cost = $1,500 + $36×x

Besame Beauty; Cost = $2,200 + $44×x

4)  For Alcone Company, we have;

Profit = $9 × x - $1,500

For  Besame Beauty, we have;

Profit = $11 × x - $2,200

5) For Alcone Company;

Profit= $525

For Besame Beauty;

Profit = $275

6) For Alcone Company;

Profit = -$150

For Besame Beauty;

Profit  -$550

7) Order of operations is used to ensure that the revenue is first calculated before the cost is subtracted to find the costs

8) In order to find the number of tubes that the company would need to manufacture in order to have a profit of greater than 0, we equate the expression using the inequality of greater than 0 to find the value of x that must be surpassed to have a profit greater than 0

9) For Alcone Company;

The profit will be > 0 at x = 167 tubes

For Besame Beauty;

The profit will be > 0 at x = 201 tubes

Step-by-step explanation:

The given parameters are;

The Alcone Company

The price at which the shade of lip color is sold = $45 per tube

The cost incurred to make  the lip color = $36 per tube

The monthly manufacturing cost of manufacturing the lip color = $1,500

For Besame Beauty

The price at which the shade of lip color is sold = $55 per tube

The cost incurred to make  the lip color = $44 per tube

The monthly manufacturing cost of manufacturing the lip color = $2,200

1. The formula for finding the profit is given as follows;

Profit =  Revenue - Cost

Revenue = Sale price × Number of tubes sold

Cost = The monthly manufacturing cost + The cost incurred to make the lip color × Number of tubes

2. The expression for revenue for the Alcone Company is given as follows;

Revenue = $45 × x

The expression for revenue for the Besame Beauty is given as follows;

Revenue = $55 × x

3. The expression for the cost for the manufacture of the lip color by the Alcone Company per month is given as follows;

Cost = $1,500 + $36×x

The expression for the cost for the manufacture of the lip color by the Besame Beauty per month is given as follows;

Cost = $2,200 + $44×x

4)  For Alcone Company, we have;

Revenue = $45 × x

Cost = $1,500 + $36×x

By transitive property and distributive property, we have

Profit =  Revenue - Cost = $45 × x - ($1,500 + $36×x) = $9 × x - $1,500

Profit = $9 × x - $1,500

For  Besame Beauty, we have;

Revenue = $55 × x

Cost = $2,200 + $44×x

By transitive property and distributive property, we have;

Profit =  Revenue - Cost = $55 × x - ($2,200 + $44×x) = $11 × x - $2,200

Profit = $11 × x - $2,200

5) With the number of tubes produced = 225 tubes, we have;

For Alcone Company;

Profit = $9 × x - $1,500 = $9 × 225 - $1,500 = $525

ForBesame Beauty;

Profit = $11 × x - $1,500 = $11 × 225 - $2,200 = $275

6) With the number of tubes produced = 150 tubes, we have;

For Alcone Company;

Profit = $9 × x - $1,500 = $9 × 150 - $1,500 = -$150

For Besame Beauty;

Profit = $11 × x - $2,200 = $11 × 150 - $2,200 = -$550

7) Order of operations is used to ensure that the revenue is first calculated before the cost is subtracted to find the costs

8) In order to find the number of tubes that the company would need to manufacture in order to have a profit of greater than 0, we equate the expression using the inequality of greater than 0 to find the value of x that must be surpassed to have a profit greater than 0

9) For Alcone Company;

Profit = $9 × x - $1,500 >0

$9 × x  >0 + $1,500

$9 × x  > $1,500

x > $1,500/$9

x > 500/3

x > [tex]166\frac{2}{3}[/tex]

Therefore, the profit will be > 0 at x = 167 tubes

For Besame Beauty;

Profit = $11 × x - $2,200 > 0

$11 × x  > 0 + $2,200

$11 × x  > $2,200

x > $2,200/$11

x > 200

Therefore, the profit will be > 0 at x = 201 tubes

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1. Given: AB = 64; M lies on the line AB

AM = 4x + 4 BM= 6x-10

Prove: M is a midpoint.

Statements: Reason:
1) M lies on AB 1) Given
AB= 64
2) AM+MB=AB 2) ?

3) 4x+4+6x-10=64 3) ?

4) 10x- 6 = 64 4) ?

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Reasoning bank for #1

Addition Property of equality
Combine like terms
Definition of midpoint.
Division property of equality
Segment addition postulate

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