Answer :
Answer:
388,500 Dollars
Step-by-step explanation:
This is a problem which can be solved by using sequences.
The total number of days is 30. Let us say n=30
Now we see that for each day that passes by there is decrease in s by a quantity equal to 200
for example s(1) = 29000-200(1) = 28800
&
s(2) = 29000-200(2) = 28600
So difference between s(1) and s(2) = 200 let us call it d
For such a decreasing arithmetic sequence we can use the following formula to sum up all the spaced used over 30 days:
[tex]sum = \frac{t}{2} (2s(1) + (t-1)d)[/tex]
where s(1) = 28800
t=30
d= -200 (since it is decreasing)
Putting the above in the equation we get
Total space used = 777,000 Cubic Feet
Price per 10 cubic feet = 5 Dollars
Total Price = (777,000*5)/10 = 388,500 USD
The calculation shows that the company will pay $11,655,000 for storage over 30 days.
The question asks us to calculate the total cost that a company will pay for storage in a warehouse for 30 days, given that the cost is $5 per day for every 10 cubic feet and that the space used per day is a function of time represented by s(t) = 29000 - 200t.
First, we need to find the total cubic feet used over 30 days by summing up s(t) for each day from t=1 to t=30. This is:
S(1) + S(2) + ... + S(30). After calculating the sum, we convert the total cubic feet into units of 10 cubic feet, as the warehouse charges per 10 cubic feet. Then, multiply this number by $5 to get the daily cost. Finally, we multiply this daily cost by 30 to find the total amount paid over 30 days.
To calculate it completely, we notice that s(t) forms an arithmetic series, where each term decreases by 200 cubic feet from the previous day. The formula for the sum of the first n terms of an arithmetic series is S = n/2 * (a1 + an), where a1 is the first term and an is the nth term. In this case, a1 = s(1) = 29000 - 200(1) and an = s(30) = 29000 - 200(30).
Calculating this sum will give us the total cubic feet used over 30 days, which we then use to compute the cost as described above.
To illustrate, let's calculate S = 30/2 * (s(1) + s(30)). s(1) = 29000 - 200(1) = 28800 and s(30) = 29000 - 200(30) = 23000. Thus, S = 15 * (28800 + 23000) = 15 * (51800) = 777000 cubic feet. Next, we divide this sum by 10 to determine the number of units: 777000/10 = 77700.
We then calculate the daily cost of these units: 77700 * $5. The total cost for 30 days is 77700 * $5 * 30 which equals $11,655,000.
Therefore, the company pays $11,655,000 for the storage space over 30 days.
