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.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 106P
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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.
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Vertical Parabola
Horizontal Parabola
Point
No Solution
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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
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