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2nd Business Model using a profit function

when minimum wage is $11.50/ hour.

 

 

Profit function is "P(x)" 

 

P(x) = 3x – 100

 

Step 0: Replace the x in the inequality representing the lowest sales (60) and highest sales (130) with P(x) which represents the profit function equation "3x-100."

60

<

P(x)

<

130

           

Step 1: Insert the Profit function in the space in between the inequality representing the lowest daily sales (60) and highest daily sales (130).

60

<

3x - 100

<

130

           

Step 2: Add 100 to both sides of the inequality and the middle term.

60 +100

<

3x +100

<

130 + 100

         

Step 3: Combine like terms with addition.

160

<

3x

<

230

         

Step 4: To get "x" by itself in the middle divide both sides and the middle term by 3.

160

3

<

3x

3

<

230

3

         

Step 5: Simplify

54

<

x

<

77

 

This math shows that with higher costs caused by raising minimum wage, between 54 and 77 sandwiches must be sold per day to have a daily profit of between $60 and $130 at $6.50 per sandwich.

A way you can check this solution is by entering the profit function in a graphing calculator in the Graph mode, which requires choosing relevant graphing-window settings that fit the x-domain and y-range of the problem, and then selecting the trace button and tracing along the line of the graph until you reach the x value 54, where you will see a y value of 60 and for x value 77 you will see a y-value of 130.

 
by Andrea Boggs