A small fast-food restaurant invests $4,000 to produce a new food item that will sell for $4.59. Each item can be produced for $2.19.
(a) How many items must be sold to break even? (Round your answer to the nearest whole number.)
items
(b) How many items must be sold to make a profit of $5,500? (Round your answer to the nearest whole number.)
items
revenue = 4.59 n
cost = 4000 + 2.19 n
to break even:
4.59 n = 4000 + 2.19 n
profit = revenue - cost
5500 = 4.59 n - 4000 - 2.19 n
Thank you so very much Damon!!!! :-)
To find the answers to these questions, we need to understand the concepts of breaking even and calculating profit. The break-even point is the point at which total revenue equals total costs, indicating that there is neither profit nor loss. Calculating the profit involves subtracting the total cost from the total revenue.
In this case, the total cost includes the initial investment and the cost to produce each item, while the total revenue is the selling price per item multiplied by the number of items sold.
Let's calculate the answers to the given questions.
(a) To find the number of items that must be sold to break even, we can set up an equation and solve for the number of items.
Total Cost = Total Revenue
Cost to produce each item * Number of items = Selling price per item * Number of items
Now let's substitute the given values:
$2.19 * Number of items = $4.59 * Number of items
To solve for the number of items, we subtract $2.19 * Number of items from both sides:
$0 = $4.59 * Number of items - $2.19 * Number of items
Simplifying the equation:
$0 = $2.40 * Number of items
To solve for the number of items, we divide both sides by $2.40:
Number of items = $0 / $2.40
Since dividing by zero is undefined and we can't have a negative number of items, we can conclude that there is no break-even point in this scenario.
(b) To find the number of items that must be sold to make a profit of $5,500, we can set up another equation and solve for the number of items.
Total Profit = Total Revenue - Total Cost
Now let's substitute the given values:
$5,500 = ($4.59 * Number of items) - ($2.19 * Number of items)
To solve for the number of items, we subtract ($2.19 * Number of items) from both sides:
$5,500 = ($4.59 - $2.19) * Number of items
Simplifying the equation:
$5,500 = $2.40 * Number of items
To solve for the number of items, we divide both sides by $2.40:
Number of items = $5,500 / $2.40
Using a calculator, we can evaluate this division and round the result to the nearest whole number. The number of items required to make a profit of $5,500 is the rounded answer.
Please note that the answer to part (a) is not possible due to the nature of the given information. Only part (b) can be accurately calculated.