Question

jonas has been selling shirts in the art on the rocks area at the festival for the past 25 years. his total costs (production of the shirts plus 15% of all sales to the festival) and the revenue he receives from sales (he has a variable pricing scheme) are shown on the graph below.

graph of revenue (a parabola) and cost (a line) with x-axis as quantity (100s) and y-axis as value ($), with revenue peaking and intersecting cost at two points

a) what are the solutions to this system? give answers to the nearest hundred.
b) interpret the solution and its importance to jonas.
c) you can determine the profit using the equation profit = revenue − cost. use the graph to estimate the quantity that gives the greatest profit. explain why this is the quantity that gives him the most profit.

Explanation:

Answer:

(1000, 8000) and (10000, 8000)
The solutions are the break - even points. At these quantities, Jonas's revenue equals his cost (he makes no profit and no loss).
600 shirts. The profit is maximum when the vertical distance between the revenue and cost curves is the greatest. At \(x = 6\) (600 shirts), the revenue is much higher than the cost.