A farmer has 500 acres of arable land on which he wants to plant potatoes and corn. The farmer has $40,000 available for planting and $30,000 for fertilizer. Planting 1 acre of potatoes costs $90, and planting 1 acre of corn costs $50. Fertilizer costs $30 for 1 acre of potatoes and $80 for 1 acre of corn. (a) Find a system of inequalities that describes the number of acres of each crop that the farmer can plant with the available resources. (Let x and y be the numbers of acres of potatoes and corn, respectively.) x + y ≤ 500 ≤ 40,000 ≤ 30,000 x ≥ 0 , y ≥ 0 Graph the feasible region. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties. (b) Can the farmer plant 290 acres of potatoes and 160 acres of corn? YesNo (c) Can the farmer plant 125 acres of potatoes and 350 acres of corn? YesNo
A farmer has 500 acres of arable land on which he wants to plant potatoes and corn. The farmer has $40,000 available for planting and $30,000 for fertilizer. Planting 1 acre of potatoes costs $90, and planting 1 acre of corn costs $50. Fertilizer costs $30 for 1 acre of potatoes and $80 for 1 acre of corn. (a) Find a system of inequalities that describes the number of acres of each crop that the farmer can plant with the available resources. (Let x and y be the numbers of acres of potatoes and corn, respectively.) x + y ≤ 500 ≤ 40,000 ≤ 30,000 x ≥ 0 , y ≥ 0 Graph the feasible region. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties. (b) Can the farmer plant 290 acres of potatoes and 160 acres of corn? YesNo (c) Can the farmer plant 125 acres of potatoes and 350 acres of corn? YesNo
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Question
A farmer has 500 acres of arable land on which he wants to plant potatoes and corn. The farmer has $40,000 available for planting and $30,000 for fertilizer. Planting 1 acre of potatoes costs $90, and planting 1 acre of corn costs $50. Fertilizer costs $30 for 1 acre of potatoes and $80 for 1 acre of corn.
(a) Find a system of inequalities that describes the number of acres of each crop that the farmer can plant with the available resources. (Let x and y be the numbers of acres of potatoes and corn, respectively.)
Graph the feasible region.
(b) Can the farmer plant 290 acres of potatoes and 160 acres of corn?
(c) Can the farmer plant 125 acres of potatoes and 350 acres of corn?
| x + y | ≤ | 500 |
|
|
≤ | 40,000 |
|
|
≤ | 30,000 |
| x ≥ 0 | , | y ≥ 0 |
Graph the feasible region.
Selection Tool
Line
Ray
Segment
Circle
Vertical Parabola
Horizontal Parabola
Point
No Solution
Help
25
50
75
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
25
50
75
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
Clear Graph
Delete Layer
Fill
WebAssign Graphing Tool
Graph LayersToggle Open/Closed
- After you add an object to the graph you can use Graph Layers to view and edit its properties.
(b) Can the farmer plant 290 acres of potatoes and 160 acres of corn?
YesNo
(c) Can the farmer plant 125 acres of potatoes and 350 acres of corn?
YesNo
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 5 images
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Purchasing and Supply Chain Management
Operations Management
ISBN:
9781285869681
Author:
Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:
Cengage Learning
Production and Operations Analysis, Seventh Editi…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.