A company produces two types of drills, a cordless model and a corded model. The cordless model requires 3 hours, and the corded-type drill requires 1 hours to make. The company has 180 work hours per day for manufacturing. The factory has space for storage of 140 drills per day. Let z = the number of cordless drills produced per day and y = the number of corded drills produced per day. Write the system of inequalities for these con ≤180 Assembly: 3x+y constraints: Storage: x+y ≤140 Graph the feasible region for this system of inequalities. Note: To get the correct feasible region, you need to also include the non-negative constraints on your graph (z >0 and y ≥ 0). These will give you boundary lines on the x-axis and y-axis.
A company produces two types of drills, a cordless model and a corded model. The cordless model requires 3 hours, and the corded-type drill requires 1 hours to make. The company has 180 work hours per day for manufacturing. The factory has space for storage of 140 drills per day. Let z = the number of cordless drills produced per day and y = the number of corded drills produced per day. Write the system of inequalities for these con ≤180 Assembly: 3x+y constraints: Storage: x+y ≤140 Graph the feasible region for this system of inequalities. Note: To get the correct feasible region, you need to also include the non-negative constraints on your graph (z >0 and y ≥ 0). These will give you boundary lines on the x-axis and y-axis.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem Description**
A company produces two types of drills: a cordless model and a corded model. The cordless model requires 3 hours to produce, while the corded model requires 1 hour. The company has a total of 180 work hours available per day for manufacturing. Additionally, the factory has storage space for a maximum of 140 drills per day.
**Variables**
Let \( x \) represent the number of cordless drills produced per day and \( y \) represent the number of corded drills produced per day.
**Constraints**
The system of inequalities for these constraints is as follows:
1. **Assembly Constraint**:
\[
3x + y \leq 180
\]
2. **Storage Constraint**:
\[
x + y \leq 140
\]
**Graphical Representation**
To find the feasible region, graph these inequalities on the coordinate plane. Additionally, apply non-negative constraints (\( x \geq 0 \) and \( y \geq 0 \)) for a realistic production scenario.
**Graph Explanation**
- The graph below is set up with \( x \)-axis representing the number of cordless drills and \( y \)-axis representing the number of corded drills.
- The lines represented by the inequalities form boundaries on this plane.
- The feasible region is where these boundaries intersect and all conditions are satisfied. This region must also lie in the first quadrant due to the non-negativity constraints.
Make sure to clearly label the axes and mark intersecting points to aid in interpretation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e471a5e-2c1f-43a0-a51a-181260b6660a%2F89652e3a-f077-469d-accc-e82f20e3879f%2Fga0fp1c_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description**
A company produces two types of drills: a cordless model and a corded model. The cordless model requires 3 hours to produce, while the corded model requires 1 hour. The company has a total of 180 work hours available per day for manufacturing. Additionally, the factory has storage space for a maximum of 140 drills per day.
**Variables**
Let \( x \) represent the number of cordless drills produced per day and \( y \) represent the number of corded drills produced per day.
**Constraints**
The system of inequalities for these constraints is as follows:
1. **Assembly Constraint**:
\[
3x + y \leq 180
\]
2. **Storage Constraint**:
\[
x + y \leq 140
\]
**Graphical Representation**
To find the feasible region, graph these inequalities on the coordinate plane. Additionally, apply non-negative constraints (\( x \geq 0 \) and \( y \geq 0 \)) for a realistic production scenario.
**Graph Explanation**
- The graph below is set up with \( x \)-axis representing the number of cordless drills and \( y \)-axis representing the number of corded drills.
- The lines represented by the inequalities form boundaries on this plane.
- The feasible region is where these boundaries intersect and all conditions are satisfied. This region must also lie in the first quadrant due to the non-negativity constraints.
Make sure to clearly label the axes and mark intersecting points to aid in interpretation.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 10 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
