Unit 4 Portfolio Part 1
You want to start a bakery business to earn money. The total amount of money you will invest is $10,000. You will be selling cakes. It will cost you $14 to make each cake.
b)
Solve this inequality and choose the graph of the solution.
* Make sure to round to the nearest dollar.
Do not include dollar signs in the solution
Let's define a variable for the number of cakes you will make and sell. Let's call this variable "x".
To find the maximum number of cakes you can make and sell within your budget, we need to solve the inequality:
14x ≤ 10,000
Dividing both sides of the inequality by 14, we get:
x ≤ 714.29
Since we can't make or sell a fractional number of cakes, we round down to the nearest whole number:
x ≤ 714
Therefore, the maximum number of cakes you can make and sell within your budget is 714.
Now let's graph the solution on a number line. We'll represent the number of cakes on the horizontal axis:
|---------------------------------------------------(714)--------------------------------------------------->
The closed circle on 714 indicates that it is included in the solution, because it is less than or equal to. Since we can't have a fraction of a cake, we don't include any numbers beyond 714.
This means that any number of cakes less than or equal to 714 is within your budget.
To solve the inequality, we need to consider the cost of making each cake and the total amount of money available for investment.
The total amount available for investment is $10,000, and each cake costs $14 to make.
Let's use the variable 'x' to represent the number of cakes sold.
The cost to make 'x' cakes is given by the equation:
Cost = $14 * x
The inequality we need to solve is:
$14 * x ≤ $10,000
We can solve this inequality by dividing both sides of the inequality by $14, giving us:
x ≤ $10,000 / $14
To find the graph of the solution, we can plot the points (x, y) where x represents the number of cakes sold, and y represents the cost of making the cakes.
By substituting the values in the inequality, we get:
x ≤ 714.2857
Rounding down to the nearest whole number, we get:
x ≤ 714 cakes.
To graph this inequality, we can draw a number line and mark a closed circle at 714. Then, draw an arrow pointing to the left to represent all values less than or equal to 714.
The graph of the solution looks like this:
-----------•----->
0 714
Therefore, the graph of the solution is a number line from 0 to the closed circle at 714, with an arrow pointing to the left.
To solve this inequality, we need to consider the investment and costs involved in the bakery business. Let's denote the number of cakes sold as "x".
The total amount invested is $10,000, and it costs $14 to make each cake. Therefore, the total cost of making the cakes is 14x.
For the bakery business to be profitable, the revenue from selling the cakes should be greater than the cost of making them. In other words, the total revenue should be greater than the total cost.
Since the cost of making x cakes is 14x, the revenue can be calculated as the selling price of each cake multiplied by the number of cakes sold. However, we don't have information about the selling price of each cake. Therefore, we cannot solve the equation directly.
However, we can still find the range of values for the selling price that would make the bakery business profitable. Let's assume the selling price per cake is "p" dollars. The revenue from selling x cakes would be px.
Now, the inequality for the profitability of the bakery business can be written as:
px > 14x
To solve this inequality, we can divide both sides by x (assuming x > 0) without changing the direction of the inequality:
p > 14
This means that for the bakery business to be profitable, the selling price per cake must be greater than $14.
Since we don't have the exact selling price, we cannot find the exact solution. However, we can graphically represent the solution on a number line or interval notation.
Graphically, we would graph the inequality p > 14 on a number line. Since there is no specific range mentioned in the problem, we would shade the region to the right of 14 (excluding 14 itself).
Here is a rough representation of this solution graphically:
-------|---------|---------------------
0 14
The shaded region represents the values for p (selling price per cake) that would make the bakery business profitable.
Note: Please remember that this is a generalized solution, and without specific information about the selling price, we cannot determine the exact solution.