Final Answer:
At the end of the week, there is a shortage of 12,000 paper cups, indicating an insufficient initial supply or an overestimation of cup usage. It is estimated that approximately 2,000 cups were used on Thursday, assuming even distribution of usage throughout the week.
Explanation:
Let's address this by recalculating the number of cups left at the end of the week and estimating the number of cups used on Thursday.
Calculation:
1. Cups Delivered: 2,000 at a time.
2. Days in a Week: 7 days.
If cups are delivered 2,000 at a time and used evenly each day, the total number of cups used during the week is

Now, to find the number of cups left at the end of the week, subtract the total cups used from the initial supply:
![\[ \text{Cups Left} = \text{Initial Supply} - \text{Total Cups Used} \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/y31beq1crb2kzkxgf8oufgj5z1sk2d64ws.png)
![\[ \text{Cups Left} = 2,000 - 14,000 = -12,000 \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/tdu1pfjzdxyq9kf82nx9bmua17e2k12pzm.png)
The negative value indicates that there is a shortage of 12,000 cups at the end of the week, not a surplus as mentioned in the previous response.
To estimate the number of cups used on Thursday, assuming even distribution, we calculate
of the total cups used during the week:
![\[ \text{Cups Used on Thursday} = (1)/(7) * 14,000 = 2,000 \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/1o4oniwxin0w1f65hhjjg0gem31n4p0p4j.png)
In this summary At the end of the week, there is a shortage of 12,000 paper cups, indicating an insufficient initial supply or an overestimation of cup usage. It is estimated that approximately 2,000 cups were used on Thursday, assuming even distribution of usage throughout the week.