Question:
A company produces boxes of DVDs at a rate of 52 boxes per hour they begin to produce boxes when they first opened for the day and after 3 hours have 400 boxes in stock.
- How many boxes were in stock when they opened?
- Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h.
- Use your model to predict the number of boxes in stock at the end of an 8 hour shift.
Answer:
1. [tex]Initial = 244[/tex]
2. [tex]b = 244 + 52h[/tex]
3. 660 boxes
Step-by-step explanation:
Given
[tex]Rate = 52\ per\ hour[/tex]
[tex]Total\ boxes\ in\ 3\ hours = 400[/tex]
Solving (a): Initial Number of boxes
First, we calculate the number of boxes made in 3 hours
[tex]Boxes = Rate * Hours[/tex]
[tex]Boxes = 52 * 3[/tex]
[tex]Boxes = 156[/tex]
If they had 400 boxes at the 3rd hour.
Then, the number of boxes when they opened is:
[tex]Initial = 400 - 156[/tex]
[tex]Initial = 244[/tex]
Solving (b): Linear function
[tex]b = boxes[/tex]
[tex]h = hours[/tex]
Since, we have the rate and the initial number of boxes.
The linear function is:
[tex]Boxes = Initial + Rate * Hours[/tex]
i.e.
[tex]b = 244 + 52 * h[/tex]
[tex]b = 244 + 52h[/tex]
Solving (c): Boxes at the end of the 8th hour
We have:
[tex]b = 244 + 52h[/tex]
In this case:
[tex]h = 8[/tex]
Substitute 8 for h
[tex]b = 244 + 52 * 8[/tex]
[tex]b = 244 + 416[/tex]
[tex]b = 660[/tex]
Hence, there are 660 boxes at the end of the 8th hour
