the alcone company\nthis company makes a popular shade of lip color that retails for $45 per tube. the lip…

the alcone company\nthis 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.\nbesame beauty\na 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.\nuse the information given to explore some of the mathematical concepts you have practiced so far by answering the questions below.\n1. 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.\n2. write an expression that each company can use to describe the amount of money they will earn as revenue from selling their lip colors. let x represent the number of tubes of lip color each company sells.

the alcone company\nthis 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.\nbesame beauty\na 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.\nuse the information given to explore some of the mathematical concepts you have practiced so far by answering the questions below.\n1. 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.\n2. write an expression that each company can use to describe the amount of money they will earn as revenue from selling their lip colors. let x represent the number of tubes of lip color each company sells.

Answer

  1. Let (x) be the number of tubes sold. For a company, profit (P=( \text{Selling price per unit}-\text{Cost per unit})x-\text{Monthly fixed - costs}). Let (s) be the selling price per unit, (c) be the cost per unit, and (F) be the monthly fixed - costs. So the formula for profit is (P=(s - c)x−F). This formula works for both companies because profit is calculated as the difference between total revenue (selling price per unit times the number of units sold) and total cost (cost per unit times the number of units sold plus fixed monthly costs).
    • For The Alcone Company, the revenue (R_{A}=45x).
    • For Besame Beauty, the revenue (R_{B}=55x).

Answer:

  1. (P=(s - c)x−F)
  2. (a) (R_{A}=45x)
    (b) (R_{B}=55x)