Jackson Farms has allotted a certain amount of land for cultivating soybeans, corn, and wheat. Cultivating 1 acre of soybeans requires 2 labor-hours, and cultivating 1 acre of corn or wheat requires 6 labor-hours. The cost of seeds for 1 acre of soybeans is $12, the cost for 1 acre of corn is $20, and the cost for 1 acre of wheat is $8. If all resources are to be used, how many acres of each crop should be cultivated if the following hold? (a) 1200 acres of land are allotted, 4800 labor-hours are available, and $15,600 is available for seeds. acres of soybeans acres of corn acres of wheat (b) 1200 acres of land are allotted, 5200 labor-hours are available, and $16,400 is available for seeds. acres of soybeans acres of corn acres of wheat

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Jackson Farms Problem: Optimization of Crop Cultivation**

Jackson Farms has allotted a certain amount of land for cultivating soybeans, corn, and wheat. The requirements for cultivation are as follows:

- Cultivating 1 acre of soybeans requires 2 labor-hours.
- Cultivating 1 acre of corn or wheat requires 6 labor-hours.
- The cost of seeds is $12 per acre for soybeans, $20 per acre for corn, and $8 per acre for wheat.

Given these constraints, the task is to determine the number of acres for each crop that should be cultivated under two different scenarios where all resources (land, labor-hours, and seed budget) are fully utilized.

**Scenario (a):**
- Total land available: 1200 acres
- Total labor-hours available: 4800
- Total budget for seeds: $15,600

Calculate the acres for:
- Soybeans
- Corn
- Wheat

**Scenario (b):**
- Total land available: 1200 acres
- Total labor-hours available: 5200
- Total budget for seeds: $16,400

Calculate the acres for:
- Soybeans
- Corn
- Wheat

**Instructions:**
Input the calculated acres for soybeans, corn, and wheat based on the given constraints for each scenario.
Transcribed Image Text:**Jackson Farms Problem: Optimization of Crop Cultivation** Jackson Farms has allotted a certain amount of land for cultivating soybeans, corn, and wheat. The requirements for cultivation are as follows: - Cultivating 1 acre of soybeans requires 2 labor-hours. - Cultivating 1 acre of corn or wheat requires 6 labor-hours. - The cost of seeds is $12 per acre for soybeans, $20 per acre for corn, and $8 per acre for wheat. Given these constraints, the task is to determine the number of acres for each crop that should be cultivated under two different scenarios where all resources (land, labor-hours, and seed budget) are fully utilized. **Scenario (a):** - Total land available: 1200 acres - Total labor-hours available: 4800 - Total budget for seeds: $15,600 Calculate the acres for: - Soybeans - Corn - Wheat **Scenario (b):** - Total land available: 1200 acres - Total labor-hours available: 5200 - Total budget for seeds: $16,400 Calculate the acres for: - Soybeans - Corn - Wheat **Instructions:** Input the calculated acres for soybeans, corn, and wheat based on the given constraints for each scenario.
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