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Sergio039 [100]
3 years ago
14

In efforts of improving their orofit margins, a company is considering creating their own manufacturing plant for their product.

It had a start-up cost of 25,000 to build the plant. This plant will drop the production cost down to $15 per item. If each item sells for $50, then how many items would it take to get an overall profit of $100,000 for the year?
Mathematics
1 answer:
Trava [24]3 years ago
7 0

Answer:

To get an overall profit of $100,000, then 3,571 items is needed to be produced

Step-by-step explanation:

Mathematically;

Profit = Revenue - Production cost

In the question, we are told that the profit we are expecting is $100,000

Let the number of items to be produced for sales be x items

Now let’s look at the production cost ;

The production cost will be number of items for sale * production cost = 15 * x = $15x

Now, we need to add the start-up cost to the production cost to get the total amount spent on production;

Mathematically the total amount would be = $25,000 + $15x

Let’s look at the revenue;

The revenue will be selling price of each item * price of each item;

Mathematically, that would be 50 * x = $50x

So therefore;

50x - (25,000 + 15x) = 100,000

50x -25,000 -15x = 100,000

35x = 100,000 + 25,000

35x = 125,000

x = 125,000/35 = 3571.42 which is approximately 3,571 items

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<h2>18</h2>

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3 years ago
A geometric sequence is defined by the general term tn = 75(5n), where n ∈N and n ≥ 1. What is the recursive formula of the sequ
andreyandreev [35.5K]
The correct answer is C) t₁ = 375, t_n=5t_{n-1}.

From the general form,
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The general form is derived from the explicit form, which is
t_n=t_1(r)^{n-1}.  We can see that r = 5; 5 has the exponent, so that is what is multiplied by every time. This gives us

t_n=t_1(5)^{n-1}

Using the products of exponents, we can "split up" the exponent:
t_n=t_1(5)^n(5)^{-1}

We know that 5⁻¹ = 1/5, so this gives us
t_n=t_1(\frac{1}{5})(5)^n&#10;\\&#10;\\=\frac{t_1}{5}(5)^n

Comparing this to our general form, we see that
\frac{t_1}{5}=75

Multiplying by 5 on both sides, we get that
t₁ = 75*5 = 375

The recursive formula for a geometric sequence is given by
t_n=t_{n-1}(r), while we must state what t₁ is; this gives us

t_1=375; t_n=t_{n-1}(5)

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