Cost, Revenue, Profit

You decide to begin selling bottles of water at the local carnival. Your cost for each bottle of water is $2.02 plus you have to pay a fixed weekly fee of $250 for the booth. Your plan is to sell each bottle of water for $3.40.

1 - expression to represent your total costs for the week if you sell n bottles of water.

Total Costs =

2 - expression to represent the revenue from the sale of nn bottles of water during the week.

Revenue =  

3 - expression that represents the profit for selling nn bottles of water in a given week.

Profit =  

How many bottles of water must you sell in order to make a positive profit?

In all the formulas Let x be the number of bottles sold

1.) Total Costs = $2.02x + $250

*$2.20 representing the variable cost per unit of bottle sold and the $250 as the fixed cost per week

2.) Revenue = $3.40x

*Revenue is the total proceeds from sales coming from the bottled water. So the total revenue would be the selling price of 3.40 per bottle multiplied by the number of bottles sold

3.) Profit= $3.40x - ($2.02x + $250 )

*The above equation is the combination of the revenue and cost formulas.

4.) 182 bottles or more

*To get the units to be sold for a positive profit we just have to add 1 unit to the break even units of the given cost and selling price of the problem.

Computed as:

Break even = Fixed Cost / Contribution margin per unit

= 250(Fixed cost) / 1.38 (CM per unit)*

=181.159... (but since there is no half bottles sold, we have to round it up to the nearest ones. so that is how we got the 182 bottles)

*Contribution margin per unit = Selling price per unit (3.40) - Variable cost per unit ( 2.02) = 1.38

To prove substitute 182 bottles on the profit formula in number 3

$3.40(182) - ($2.02(182) + $250 )

= 618.8 (Total Revenue) - 617.64 (Total cost consisting of variable and fixed)

= 1.16 (Profit)