Inventory Build-Up: A 24-hour donut shop starts each day with fresh donuts. They begin making the day's fresh donuts at 4:00 a.m. and continue until 3:00 p.m. when they have enough donuts to satisfy the entire day's demand until the next day's batch starts. Their inventory is zero at 4:00 a.m. when they start making the day's fresh donuts; and their donut production machine completes the production process for 8 donuts every 15 seconds. The table below shows the demand they experience throughout the day: Time Block Hourly Demand 4:00 a.m. - 6:00 a.m. 300 6:00 a.m. - 10:00 a.m. 2000 10:00 a.m. - 12:00 p.m. 1200 12:00 p.m. - 1:00 p.m. 1600 800 1:00 p.m. - 5:00 p.m. 5:00 p.m. - 8:00 p.m. 1200 8:00 p.m. - 10:00 p.m. 980 10:00 p.m. - 1:00 a.m. 1000 1:00 a.m. - 4:00 a.m. 200 What is their inventory at 6 p.m.?

Inventory Build-Up: A 24-hour donut shop starts each day with fresh donuts. They begin making the day's fresh donuts at 4:00 a.m. and continue until 3:00 p.m. when they have enough donuts to satisfy the entire day's demand until the next day's batch starts. Their inventory is zero at 4:00 a.m. when they start making the day's fresh donuts; and their donut production machine completes the production process for 8 donuts every 15 seconds. The table below shows the demand they experience throughout the day: Time Block Hourly Demand 4:00 a.m. - 6:00 a.m. 300 6:00 a.m. - 10:00 a.m. 2000 10:00 a.m. - 12:00 p.m. 1200 12:00 p.m. - 1:00 p.m. 1600 800 1:00 p.m. - 5:00 p.m. 5:00 p.m. - 8:00 p.m. 1200 8:00 p.m. - 10:00 p.m. 980 10:00 p.m. - 1:00 a.m. 1000 1:00 a.m. - 4:00 a.m. 200 What is their inventory at 6 p.m.?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

**Inventory Build-Up:**

A 24-hour donut shop starts each day with fresh donuts. They begin making the day's fresh donuts at 4:00 a.m. and continue until 3:00 p.m., when they have enough donuts to satisfy the entire day's demand until the next day's batch starts. Their inventory is zero at 4:00 a.m. when they start making the day's fresh donuts; and their donut production machine completes the production process for 8 donuts every 15 seconds. The table below shows the demand they experience throughout the day:

| Time Block | **Hourly Demand** |
|----------------------|-------------------|
| 4:00 a.m. - 6:00 a.m.| 300 |
| 6:00 a.m. - 10:00 a.m.| 2000 |
| 10:00 a.m. - 12:00 p.m.| 1200 |
| 12:00 p.m. - 1:00 p.m.| 1600 |
| 1:00 p.m. - 5:00 p.m.| 800 |
| 5:00 p.m. - 8:00 p.m.| 1200 |
| 8:00 p.m. - 10:00 p.m.| 980 |
| 10:00 p.m. - 1:00 a.m.| 1000 |
| 1:00 a.m. - 4:00 a.m.| 200 |

**Question:**
What is their inventory at 6 p.m.?

---

To find the inventory at 6 p.m., calculate the donut production rate and subtract the cumulative demand by 6 p.m.

- **Production Rate Calculation:**
- The machine produces 8 donuts every 15 seconds.
- In one hour (3600 seconds), it produces: $ \frac{3600 \, \text{seconds}}{15 \, \text{seconds}} \times 8 \, \text{donuts} = 1920 \, \text{donuts per hour} $.

- **Demand from 4:00 a.m. to 6:00 p.m.:**
- **4:00 a.m. - 6:00 a.m.:** 300 donuts
- **6:00 a.m. - 10:00 a.m.:**

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