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

madelyn 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.

madelyn 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

Explanation:

Step1: Identify the slope - intercept form

The cost function has 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 $b = 800$. This is the fixed cost (when $p = 0$), so $b=800$.

Step3: Calculate the slope

Pick two points on the line, say $(0,800)$ and $(10,2600)$. The slope $m=\frac{\Delta C}{\Delta p}=\frac{2600 - 800}{10-0}=\frac{1800}{10}=180$.

Step4: Write the cost equation

Substitute $m = 180$ and $b = 800$ into $C=mp + b$. The equation is $C = 180p+800$.

Step5: Interpret the slope

The slope $m = 180$ means that for each additional phone produced, the total cost increases by $$180$. This is the variable cost per phone (cost of materials and labor per phone).

Answer:

The equation for $C$ is $C = 180p + 800$. The slope of the graph is $180$, and it represents the cost per phone produced for materials and labor.