A firm believes the sales volume (S) of its product depends on its unit selling price (P) and can be determined from the equation P = $100 - S. The cost (C) of producing the product is $1000 + l0S.
a) Draw a graph with the sales volume (S) from 0 to 100 on the x axis, and total cost and total income from 0 to 2500 on the y axis. On the graph –draw the line C = $1000 + l0 S. Then plot the curve of total income [which is sales volume (S) x unit selling price ($100 - S)]. Mark the breakeven points on the graph
b) Determine the breakeven point (lowest sales volume where total sales income just equals total production cost). (Hint: This may be done by trial and error or by using the quadratic equation to locate the point at which profit is zero.)
c) Determine the sales volume (S) at which the firm's profit is a maximum. (Hint: Write an equation for profit and solve it by trial and error, or as a minima-maxima calculus problem.)