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) x ≤ 714r
c) 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?
To determine the most money you can hope to earn from your business, you need to find the maximum value of the equation T = 50x.
From part b, we have the inequality x ≤ 714r, which means the quantity of cakes you can make (x) is less than or equal to 714 times the available investment amount (r).
Since you have a total investment of $10,000, we can substitute r = 10,000 in the inequality:
x ≤ 714(10,000)
x ≤ 7,140,000
So, the maximum number of cakes you can make is 7,140,000.
Now, substituting this value in the equation T = 50x:
T = 50(7,140,000)
T = 357,000,000
Therefore, the most money you can hope to earn from your business is $357,000,000.
To find the most money you can hope to earn from your business, we need to use the equation from part c, which is T = 50x.
Here, T represents the total earnings and x represents the number of cakes sold.
Now, let's use the inequality from part b, which is x ≤ 714r.
Since we are interested in the maximum earnings, we want to maximize the value of x. From the inequality, we can see that x is constrained by the value of r.
To maximize x, we need to find the largest possible integer value for r, which will give us the maximum number of cakes we can sell.
Given that you will invest $10,000 and it costs $14 to make each cake, the maximum number of cakes you can produce is $10,000 / $14 = 714.28 (approximately).
Since we can only sell whole cakes, the largest integer value for x is 714.
Plugging this value of x into the equation T = 50x, we get:
T = 50 * 714
T = 35,700
Therefore, the most money you can hope to earn from your business is $35,700.
To determine the most money you can hope to earn from your bakery business, we need to find the value of x (the number of cakes sold) that maximizes the total revenue (T).
From part b, we have the inequality x ≤ 714r, where r represents the number of times you can make cakes with your investment of $10,000.
To find the value of x that maximizes revenue, we need to find the corresponding value of r.
One way to do this is by dividing your initial investment by the cost to make each cake. So, r = $10,000 / $14 = 714.
Now, we can substitute the value of r into the equation from part c, which is T = 50x.
T = 50x
T = 50 * 714 (substituting r = 714)
T = 35,700
Therefore, the most money you can hope to earn from your bakery business is $35,700.