10. amazon tracks their inventory of boxes very closely. they start with 5,000 boxes this week and predict…

10. amazon tracks their inventory of boxes very closely. they start with 5,000 boxes this week and predict that they will use 750 boxes per day.\npart 1: assuming the usage rate of boxes stays the same, create a linear equation that can model the relationship between the number of boxes that remain in inventory, b, based on the number of days, d.\npart 2: amazon calculates that they will need to order more boxes when their inventory gets down to 1,000 boxes. explain why waiting 6 days to order new boxes would be insufficient. in your explanation, identify the last - possible day before amazon would need to order new boxes.

10. amazon tracks their inventory of boxes very closely. they start with 5,000 boxes this week and predict that they will use 750 boxes per day.\npart 1: assuming the usage rate of boxes stays the same, create a linear equation that can model the relationship between the number of boxes that remain in inventory, b, based on the number of days, d.\npart 2: amazon calculates that they will need to order more boxes when their inventory gets down to 1,000 boxes. explain why waiting 6 days to order new boxes would be insufficient. in your explanation, identify the last - possible day before amazon would need to order new boxes.

Answer

Explanation:

Step1: Define variables and create equation

Let $y$ be the number of boxes remaining in inventory. The initial number of boxes is 5000 and the rate of usage is 750 boxes per day. So the linear - equation is $y = 5000-750d$.

Step2: Solve for $d$ when $y = 1000$

Set $y = 1000$ in the equation $y = 5000 - 750d$. Then we have $1000=5000 - 750d$. First, add $750d$ to both sides: $750d+1000 = 5000$. Then subtract 1000 from both sides: $750d=5000 - 1000=4000$. Finally, divide both sides by 750: $d=\frac{4000}{750}=\frac{16}{3}\approx5.33$.

Step3: Analyze the last - possible day

Since $d=\frac{16}{3}\approx5.33$, the last possible day before Amazon needs to order new boxes is the 5th day. If they wait until the 6th day, the inventory will be $y = 5000-750\times6=5000 - 4500 = 500$ boxes, which is less than the 1000 - box threshold.

Answer:

Part 1: $y = 5000-750d$ Part 2: The last possible day is the 5th day. Waiting 6 days is insufficient because if $d = 6$, then $y=5000 - 750\times6=500$ boxes, which is less than the 1000 - box inventory threshold.