The cost and revenue functions of a company are given by the equation C(x)=30x+1000 and R(x)=70x-1000, respectively.

Question

In these equations, x is the number of items produced and sold and C(x) and R(x) are in rands.

 

8.1 Determine the profit function P(x).

8.2 What is the break-even level?

8.3 Draw a neat plot of each function indicating functions C and R on the same set of axes.

Answer 1

Profit = Revenue - Cost

P(x) = 70x - 1000 - (30x + 1000)

P(x) = 70x -1000 - 30x - 1000

P(x) = 40x - 2000

 

Break-even occurs when P(x) = 0

P(x) = 40x - 2000

0 = 40x - 2000

2000 = 40x

2000/40 = x

50 = x

 

Can't draw the plot for you on this editor.  Both C(x) and R(x) are straight lines in the form y = mx+b where m is the slope and b is the y-intercept.  C(x) has a y-intercept of 1000 and a slope of 30.  R(x) has a y-intercept of -1000 and a slope of 70.