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 >

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