11. A small country exports soybeans and flowers. Soybeans require 8 workers per acre, flowers require 12 workers per acre and 100,000 workers are available. Government contracts require that there be at least 3 times as many acres of soybeans as flowers planted. It costs $250 per acre to plant soybeans and $300 per acre to plant flowers, and there is a budget of $3 million. If the profit from soybeans is $1,800 per acre and the profit from flowers is $2,000 per acre, how many acres of each crop should be planted to maximize profit? Then find the maximum profit.

11. A small country exports soybeans and flowers. Soybeans require 8 workers per acre, flowers require 12 workers per acre and 100,000 workers are available. Government contracts require that there be at least 3 times as many acres of soybeans as flowers planted. It costs $250 per acre to plant soybeans and $300 per acre to plant flowers, and there is a budget of $3 million. If the profit from soybeans is $1,800 per acre and the profit from flowers is $2,000 per acre, how many acres of each crop should be planted to maximize profit? Then find the maximum profit.

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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

11. A small country exports soybeans and flowers. Soybeans require 8 workers per acre, flowers
require 12 workers per acre and 100,000 workers are available. Government contracts require that
there be at least 3 times as many acres of soybeans as flowers planted. It costs $250 per acre to plant
soybeans and $300 per acre to plant flowers, and there is a budget of $3 million.
If the profit from soybeans is $1,800 per acre and the profit from flowers is $2,000 per acre, how
many acres of each crop should be planted to maximize profit? Then find the maximum profit.

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