Question

Your community newspaper, The Xpress, has fixed production costs of K70 per edition, and marginal printing and distribution costs of 40n/copy. The Xpress sells for 50n/copy
a) Write down the associated cost, revenue, and profit functions. (6 marks)
b) What profit (or loss) results from the sale of 500 copies of The Xpress? (2 marks)
c) How many copies should be sold in order to break even?

Answer 1

Solution

To print $\frac{40}{n}$ Copies (x₁)

To sell $\frac{50}{n}$ Copies (x₂)

a.) Cost function (fx₁)= 70+40 x₁

Revenue function (fx₂)= 50x₂

Profit= Revenue-Cost

= $50x_2-70-40x_2= 10x_2-70$

b.) $x_2=500$

$y=10\times500-70=4930$

4930 is the amount of profit for selling 500 copies

c.) Break even points

Equate the cost function and the revenue function to get the value of x

$70+40x=50x$

$x=7$

They should sell 7 copies in order to break even.