violet is in the business of manufacturing phones. she must pay a daily fixed cost to rent the building and…

violet is in the business of manufacturing phones. she must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. let c represent the total cost, in dollars, of producing p phones in a given day. a graph of c is shown below. write an equation for c then state the slope of the graph and determine its interpretation in the context of the problem.

violet is in the business of manufacturing phones. she must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. let c represent the total cost, in dollars, of producing p phones in a given day. a graph of c is shown below. write an equation for c then state the slope of the graph and determine its interpretation in the context of the problem.

Answer

Answer:

Equation: $C = 100p+200$; Slope: $100$; Interpretation: The cost per phone produced (variable - cost per unit) is $$100$.

Explanation:

Step1: Identify the slope - intercept form

The total cost function is of the form $C=mp + b$, where $m$ is the slope and $b$ is the $y$ - intercept.

Step2: Find the $y$ - intercept

The line crosses the $C$ - axis at $(0,200)$. So, $b = 200$.

Step3: Calculate the slope

Using two points $(0,200)$ and $(1,300)$, the slope $m=\frac{C_2 - C_1}{p_2 - p_1}=\frac{300 - 200}{1-0}=100$.

Step4: Write the equation

Substitute $m = 100$ and $b = 200$ into $C=mp + b$ to get $C = 100p+200$.

Step5: Interpret the slope

In the context of the problem, the slope represents the additional cost for each additional phone produced. So, for each additional phone made, the cost increases by $$100$.