The Yin-Yang Yogurt Shoppe serves the best chocolate-vanilla frozen yogurt in the city. Each cup of yogurt sells for $4, with variable costs amounting to $2 per cup. Yin-Yang’s fixed costs equal $3,000 per month.
a. Graph Yin-Yang Yogurt Shoppe’s total costs as a function of the number of cups of yogurt sold (going from 0 to 2,500 cups of yogurt in increments of 500 cups). What does the y-intercept (i.e., the point where the total cost line crosses the y-axis) represent? What does the slope of the total cost line represent?
b. Add a plot of the Yin-Yang Yogurt Shoppe’s total revenue (as a function of the number of cups of yogurt sold) to your graph from part (a). Identify the breakeven point in your graph. Identify the profit and loss areas.
c. Construct a profit graph for the Yin-Yang Yogurt Shoppe. Form a single line that depicts Yin-Yang’s profit as a function of the number of cups of yogurt sold. What does the intercept of the profit line represent? What does the slope of the profit line represent? How do you interpret the point at which the profit line crosses the horizontal (i.e., x) axis? Identify the profit and loss areas.
d. Suppose Yin-Yang pays taxes at the rate of 40% of profit. How does this affect the profit line?
e. (Advanced) Assume you do not have unit-level data; in other words, assume you only know that Yin Yang’s monthly fixed costs equal $3,000 and that its contribution margin ratio is 50% (you gather this information from Yin Yang’s financial statements). Construct a profit graph that allows you to identify Yin Yang’s breakeven point and profit and loss areas.