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.
Solve this inequality and choose the graph of the solution
x≤714
You plan to sell each cake for $50. Write an equation that represents your total earnings, T, based on the price of your cake and how many you sell. Let x represent the number of cakes you sell.
T≤50x
Using your answer from part b and your equation from part c, what is the most money you can hope to earn from your business?
The most money you can hope to earn from your business can be found by substituting the inequality x≤714 into the equation T≤50x:
T≤50(714)
T≤35,700
Therefore, the most money you can hope to earn from your business is $35,700.
To find the most money you can hope to earn from your business, you need to determine the maximum value for T (total earnings) based on the given equation T≤50x. Since T represents the total earnings and x represents the number of cakes you sell, you want to maximize T.
To do this, you need to find the maximum value for x. Since the total amount of money you will invest is $10,000 and each cake costs $14 to make, you can calculate the maximum number of cakes you can sell by dividing the total investment by the cost of each cake:
Number of cakes = Total investment / Cost per cake
Number of cakes = $10,000 / $14 ≈ 714.29
Since you cannot sell a fraction of a cake, the maximum number of cakes you can sell is 714. So, x can have a maximum value of 714.
Now, substitute the maximum value of x (which is 714) into the equation T≤50x:
T≤50 * 714
T≤35,700
Therefore, the most money you can hope to earn from your business is $35,700.
The most money you can hope to earn from your business can be found by substituting the value of x in the equation T ≤ 50x with the maximum value of x, which is 714 (since x ≤ 714).
T ≤ 50(714)
T ≤ 35,700
Therefore, the most money you can hope to earn from your business is $35,700.
Don’t forget that at the beginning of the process you had to spend some of your own money to get started. With the costs taken into account, what was your total profit?
To calculate the total profit, we need to subtract the total cost from the total earnings.
The total cost can be calculated by multiplying the cost per cake ($14) by the number of cakes sold (x):
Total cost = $14 * x
The total earnings, T, is given by the equation T ≤ 50x.
Now, let's subtract the total cost from the total earnings to get the total profit (P):
P = T - Total cost
P = T - ($14 * x)
Substituting the value of x (714) into the equation:
P = $35,700 - ($14 * 714)
P = $35,700 - $9,996
P = $25,704
Therefore, the total profit from the bakery business, taking into account the costs, is $25,704.