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

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.

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
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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.

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