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The problem asks to model a system of inequalities based on the constraints of production for corded and cordless drills. Here's the breakdown:

### Given Information:
1. **Corded drill** takes 3 hours to manufacture.
2. **Cordless drill** takes 4 hours to manufacture.
3. Total available manufacturing hours per day: **720 hours**.
4. Total storage available per day: **190 drills**.

Let:
- \( x \) represent the number of **cordless drills** produced per day.
- \( y \) represent the number of **corded drills** produced per day.

### Constraints:

1. **Manufacturing time constraint**:
   The total time to make \( x \) cordless and \( y \) corded drills must not exceed the available 720 work hours per day. 
   \[
   4x + 3y \leq 720
   \]

2. **Storage constraint**:
   The total number of drills (corded + cordless) must not exceed 190 per day.
   \[
   x + y \leq 190
   \]

### System of Inequalities:
\[
\begin{aligned}
4x + 3y & \leq 720 \\
x + y & \leq 190
\end{aligned}
\]

Next, to graph the system of inequalities:
- You will plot the lines \( 4x + 3y = 720 \) and \( x + y = 190 \).
- Shade the region that satisfies both inequalities, which will represent the feasible production combinations of cordless and corded drills.

Would you like further assistance on how to graph this system of inequalities, or should I explain how to find the boundary lines and feasible region?

---

Here are five follow-up questions:
1. How do you determine the intercepts for each inequality when graphing?
2. What does the intersection of the two lines represent in this scenario?
3. How would you find the maximum number of cordless drills produced if no corded drills were made?
4. What does the shading of the graph represent in the context of the problem?
5. How would the system change if you had 800 work hours instead of 720?

**Tip:** When graphing inequalities, always remember to test a point (like the origin) to determine the correct side of the line to shade.

A company produces two types of drills, a corded and cordless. The cord-type drill requires 3 hours to make, and the cordless model requires 4 hours. The company has 720 work hours per day for manufacturing and daily storage of 190 drills per day. Let x = the number of cordless drills produced per day and y = the number of corded drills produced per day. Write the system of inequalities and graph it.

Learn how to model and solve a system of inequalities for a company that produces corded and cordless drills. This problem involves constraints on work hours and storage capacity, suitable for Grades 8-10. We will explore linear inequalities and how to graph the feasible region.

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