SOLUTION: a company manufacture and sells novelty mugs.The manufacturing cost consist of a fixed cost of R8000 and a variable cost of R15.00 per mug.The mugs are sold at R35.00 each.Assume a

Question 1030946: a company manufacture and sells novelty mugs.The manufacturing cost consist of a fixed cost of R8000 and a variable cost of R15.00 per mug.The mugs are sold at R35.00 each.Assume a linear profit function.
1. determine the profit function.
2. What is the break-even level?
3. Draw a graph depicting the profit function.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of novelty mugs sold.
r = revenue
c = cost
p = profit

formula for profit is p = r - c

formula for revenue is r = 35x

formula for cost is c = 8000 + 15x

when you break even, your profit is equal to 0.

formula for profit of p = r - c becomes 0 = r - c which becomes 0 = 35x - (8000 + 15x) which becomes 0 = 35x - 8000 - 15x which becomes 0 = 20x - 8000.

add 8000 to both sides of this equation to get 8000 = 20x.

solve for x to get x = 400.

you will break even when the number of units sold is 400.

revenue is 400 * 35 = 14000.
cost is 8000 + 15x = 8000 + 6000 = 14000.

profit is revenue minus cost which is equal to 0.
that's your break even point.
when x = 400.

since p = r - c which becomes p = 35x - (8000 + 15x) which becomes p = 20x - 8000 after simplification, you would set p equal to y and graph y = 20x - 8000 to graph the profit function.

the graph is shown below.

look below the graph for further comments.

$$$

the value for x are marked for 200, 400, and 600 units.

when x = 200, you take a loss of 4000 because the number of units sold at 35 times the number of units is not enough to make up for the fixed cost of 8000 plus the variable cost of 15 times the number of units.

when x = 400, you break even.

when x = 600, you take a profit of 4000 because the number of units sold at 35 times the number of units is more than enough to make up for the fixed cost of 8000 plus the variable cost of 15 times the number of units.

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