Math 132, Project 2 - Price-Supply & Profit
Please submit your project 2, along with a comprehensive list of all resources used.
This includes:
1. Citations for any outside sources (e.g., books, articles, websites) you consulted or referenced.
2. Acknowledgements for any individuals who contributed to the project, such as collaborators or mentors.
Question 1:
A coffee shop increased recently its price for a latte from \$4 per cup to \$5. In reaction, the number of lattes sold per day dropped from 50 to 40. It costs the shop about a \$1 to make a cup of latte in addition to daily fixed cost of \$57.6 to maintain the equipment.
a. Find the price-demand equation for latte and its domain, assuming that there is a linear relationship.
b. Find the daily cost function, as a function of the number of latte coffees made.
c. Find the revenue function $R(x)$ and its domain.
d. Plot $R(x)$ and $C(x)$, find the break-even points and verify your result in the plot.
e. Find the profit function $P(x)$ and its domain. Plot $P(x)$.
f. Find the price to maximize the profit. How many cups of latte are sold per day and what is the maximum daily profit?