SOLUTION: A company makes plastic containers and sells them at R45 each. The cost of production consists of a fixed cost of R28 050 and a variable cost of R12 per container. Let X be the num

Question 1161073: A company makes plastic containers and sells them at R45 each. The cost of production consists of a fixed cost of R28 050 and a variable cost of R12 per container. Let X be the number of containers produced and sold.
Write down the income equation.
Write down the cost equation.
What is the profit equation?
Hence, find the break-even production level for this company.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
p = profit
r = revenue
c = cost
x = number of units produced and sold
breakeven is when revenue = cost
r = 45 * x
c = 28050 + 12 * x
p = r minus c
p = 45 * x - (28050 + 12 * x) which becomes:
p = 45 * x - 28050 - 12 * x
combine like terms to get:
p = 33 * x - 28050
breakeven is when r = c or when p = 0, depending on which equation you use to find it.
when using r = c, breakeven is when 45 * x = 28050 + 12 * x
subtract 12 * x from both sides of this equation to get:
33 * x = 28050
solve for x to get:
x = 28050 / 33 = 850
when using p = 0, breakeven is when p = 0
p = 33 * x - 28050 becomes 0 = 33 * x - 28050
add 28050 to both sides of this equation to get:
28050 = 33 * x
solve for x to get:
x = 28050 / 33 = 850.
breakeven is when 850 units are produced and sold.
revenue = 45 * 850 = 38250
cost = 28050 + 12 * 850 = 38250
profit = revenue minus cost = 38250 - 38250 = 0.

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