**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: $15,600Calculate the acres for:- Soybeans- Corn- Wheat**Scenario (b):**- Total land available: 1200 acres- Total labor-hours available: 5200- Total budget for seeds: $16,400Calculate the acres for:- Soybeans- Corn- Wheat**Instructions:**Input the calculated acres for soybeans, corn, and wheat based on the given constraints for each scenario.

(a) Let x be the area of land in which soybeans are cultivated, y the area of land in which corns…

Answered: Jackson Farms has allotted a certain…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A patient takes vitamin pills. Each day he must have at least 420 IU of vitamin A, 8 mg of vitamin B,, and 45 mg of vitamin C. He can choose between pill 1, which contains 240 IU of vitamin A, 2 mg of vitamin By, and 5 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 2 mg of vitamin B, , and 30 mg of vitamin C. Pill 1 costs 20¢, and pill 2 costs 60¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy ……of pill 1 and…..? of pill 2. The minimum cost is $….? b. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving He is receiving ……IU of vitamin A, …….." mg of vitamin B,, and….. mg of vitamin C more than he needs.
It takes 12 units of carbohydrates and 6 units of protein to satisfy Jacob's minimum weekly requirements. The meat contains 2 units of carbohydrates and 2 units of protein per pound. The cheese contains 3 units of carbohydrates and 1 unit of protein per pound. The meat costs $3.40 per pound and the cheese costs $4.50 per pound. How many pounds of each are needed to fulfill the minimum requirements at minimum cost? What is Jacob's minimum cost? He should buy pound(s) of meat and pound(s) of cheese. (Round your answer to the nearest tenth.) The minimum cost is $. (Round to the nearest cent as needed.) ...
You run a volunteer organization to help clean up local parks. You have 108 volunteers to assign to jobs in 6 different parks. The two medium-sized parks require half as many volunteers as the one largest park. The two small parks require half as many as the medium-sized parks. And one very small park requires only one-fifth the volunteers that the largest park requires. How many volunteers should be sent to each park?
A patient takes vitamin pills. Each day he must have at least 300IU of vitamin A, 3 mg of vitamin B1, and 60 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 1 mg of vitamin B1, and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 1 mg of vitamin B1, and 40 mg of vitamin C. Pill 1 costs 25¢, and pill 2 costs 50¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy nothing of pill 1 and nothing of pill 2. The minimum cost is $ nothing. (Simplify your answers. Type integers or decimals.)
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an artist makes three types of ceramic statues( large, medium and small) at monthly cost of $880 for 250 statues. the manufacturing costs for the three types are $5,$4,$3. if the statues sell for $26, $18, and $15, respectively, how many of each type should be made to produce $4,240 in monthly revenue Large ? Medium ? Small ?
A farmer has 1,190 acres of land on which he grows corn, wheat and soybeans. It costs $45 per acre to grow corn, $60 to grow wheat, and $50 to grow soybeans. Because of market demand the farmer will grow twice as many acres of wheat as of corn. He has allocated $63,100 for the cost of growing his crops. How many acres of each crop should he plant?
both sheets are for the same problem.
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) 1100 acres of land are allotted, 4600 labor-hours are available, and $14,400 is available for seeds. acres of soybeans acres of corn acres of wheat (b) 1300 acres of land are allotted, 5400 labor-hours are available, and $17,600 is available for seeds. acres of soybeans acres of corn acres of wheat

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