Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Sydney 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 y -intercept of the graph and determine its interpretation in the context of the problem.

Sydney 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 class=

Sagot :

The equation of a line in slope-intercept form, is given by:

[tex]y=mx+b[/tex]

Where m represents the slope of the line, which is the rate of change of y with respect to x, and b represents the y-intercept of the line, which is the initial value of y when x=0.

If we use C to represent the vertical axis and p for the horizontal axis, then:

[tex]C=mp+b[/tex]

From the data on the graph, we can see that C=200 when p=0. Then, the initial value is 200, then:

[tex]b=200[/tex]

On the other hand, C=250 when p=1. Substitute this information in the equation to find the value of m:

[tex]\begin{gathered} C=mp+200 \\ \Rightarrow250=m(1)+200 \\ \Rightarrow m=50 \end{gathered}[/tex]

Therefore:

[tex]C=50p+200[/tex]

Since Sydney pays for the building and equipment regardless of the number of manufactured phones, then the initial value represents the rent of that building and equipment.

The y-intercept of the function is 200, which represents the rent of the building and equipment, or the cost of producing 0 phones.

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.