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Doss [256]
2 years ago
7

Orbital Toys sells two types of sets of magnetic spheres, silver and brass. The store owner, Lucy Ball, pays $8 and $16 for each

one set of silver magnetic spheres and brass magnetic spheres respectively. One set of silver magnetic spheres yields a profit of $3 while a set of brass magnetic spheres yields a profit of $5. Ms. Ball estimates that no more than 2000 sets of magnetic spheres will be sold every month and she does not plan to invest more than $20,000 in inventory of these sets. How many sets of each type of magnetic spheres should be stocked in order to maximize her total monthly profit? What is her maximum monthly profit?​
Mathematics
1 answer:
sdas [7]2 years ago
5 0

Answer:

The maximum profit will be reached by buying 500 brass magnetic spheres and 1500 silver magnetic spheres.

Step-by-step explanation:

In order to solve this you need to create a system of equations, with two values that will create the answer we are looking for, the thing that we don't know here is how many of each are we buying so the number of silver magnetic spheres will be represented by "y" and the brass magnetic spheres will be represented by "x".

So we know that x+y=2000

That's our first equation, our second would be the expense, which would be

8x+16y=20,000

We now just solve for one of them

x=(2000-y)

8(2000-y)+16y=20,000

16,000-8y+16y=20,000

8y=4,000

y=500

So we know that the maximum profit will be reached by buying 500 brass magnetic spheres and 1500 silver magnetic spheres.

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2. Lorena is trying to choose between two different savings accounts at H-Town Bank. She will deposit $3,500 dollars and will le
Ivahew [28]

Answer:

First of all, this question is not complete. So, we will be hypothetically create two accounts and try to choose the one with the greater profit.

Choice 1 = X = Final Amount after 12 years = $5600

Choice 2 = Y = Final Amount after 12 years = $6285.50

Hence, Lorena should choose choice 2, as it gives more profit over than choice 1.

Step-by-step explanation:

First of all, this question is not complete. So, we will be hypothetically create two accounts and try to choose the one with the greater profit.

Initial Deposit Amount = $3500

Time period = 12 years

Let's Suppose Lorena has two X and Y choices of accounts at H-town Bank.

X = simple interest of 5% over the initial amount for 12 years.

Y = Compound interest 5% over the initial amount for 12 years.

Solution:

Let's calculate the profit for choice 1 = X

Simple interest = 5%

Initial amount = $3500

Time period = 12 years

Formula = A = P (1 + rt)

where, A = Final amount after 12 years

t = time period in years  = 12

P = initial amount to be deposited = $3500

r = annual interest rate = 5%

Plug in the values to get the total amount.

A = 3500(1+0.05x12)

A = $5600 = final amount Lorena will get after 12 years.

Let's calculate the profit for choice 2 = Y

Compound interest = 5%

Initial amount = $3500

Time period = 12 years

Formula = A = P (\frac{r}{n} + 1)^{nt}

where,

A = Final amount after 12 years

t = time period in years  = 12

P = initial amount to be deposited = $3500

r = annual interest rate = 5%

n = number of times interest rate is applied or compounded. = 12

Plug in the values to get the total amount.

A = P (\frac{r}{n} + 1)^{nt}

A = $6285.50

Hence, Lorena should choose choice 2, as it gives more profit over than choice 1.

4 0
2 years ago
Easy question:
Delvig [45]

Answer:

3 hours and 45 minutes

Step-by-step explanation:

let's assume the tank has a volume of x liters.

let's assume the speed of filling it is x/6 liters per hour for A and x/10 liters per hour for B.

the formula to calculate the time is:

time = volume / speed

If the pumps work together, the total speed is x/6 + x/10, which is 16/60 x

So the time this takes is:

time = x / (16/60 x) = 60/16 hours = 3.75 hours = 3 hours and 45 minutes.

8 0
2 years ago
If Sean earns $8.50 per hour sand made a total of $80.75 today, How many hours did he work?
Serggg [28]
80.75 / 8.50 = 9.5
Sean worked 9 and a half hours.
8 0
3 years ago
Read 2 more answers
-103 = 6x + 17 equals?
Ipatiy [6.2K]

answer i think is x=43/3

4 0
2 years ago
Pls help me 20 points
nataly862011 [7]

Answer:

31/100

Step-by-step explanation:

7 0
3 years ago
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