Exercise 1 An ejidal association wishes to determine the distribution for the three different crops that it can plant for the next season on its available 900 hectares. Information on the total available and how many resources are required for each hectare of cultivation is shown in the following tables: Total available resource Water 15,000 m3 Fertilizer 5,000 kg Labor 125 day laborers Requirements per cultivated hectare Corn Soybeans Wheat Water 15 25 20 Fertilizer 5 8 7 Labor** 1/8 1/5 1/4 The data in fraction means that with one day laborer it will be possible to care for 8, 5 and 4 hectares respectively. Sales of crops 1 and 3, according to information from the Department of Agriculture, are guaranteed and exceed the capacity of the cooperative. However, soybeans must be limited to a maximum of 150 hectares. On the other hand, the profits for each hectare of crop obtained are estimated at: $7,500 for corn, $8,500 for soybeans and $8,000 for wheat. The objectives are to determine: • How many hectares of each crop must be allocated so that the profit is maximum. R= • The estimated profits for the ejidal cooperative in the next growing season. R=

Brand: MathMaster
Rating: 4.9 (255 reviews)

255

likes

1273 views

Answer to a math question Exercise 1 An ejidal association wishes to determine the distribution for the three different crops that it can plant for the next season on its available 900 hectares. Information on the total available and how many resources are required for each hectare of cultivation is shown in the following tables: Total available resource Water 15,000 m3 Fertilizer 5,000 kg Labor 125 day laborers Requirements per cultivated hectare Corn Soybeans Wheat Water 15 25 20 Fertilizer 5 8 7 Labor** 1/8 1/5 1/4 The data in fraction means that with one day laborer it will be possible to care for 8, 5 and 4 hectares respectively. Sales of crops 1 and 3, according to information from the Department of Agriculture, are guaranteed and exceed the capacity of the cooperative. However, soybeans must be limited to a maximum of 150 hectares. On the other hand, the profits for each hectare of crop obtained are estimated at: $7,500 for corn, $8,500 for soybeans and $8,000 for wheat. The objectives are to determine: • How many hectares of each crop must be allocated so that the profit is maximum. R= • The estimated profits for the ejidal cooperative in the next growing season. R=

$Expert avatar$

Murray

4.5

92 Answers

To maximize profit, the ejidal association needs to allocate the hectares for each crop based on the available resources and constraints. Let's denote: x as the hectares of corn, y as the hectares of soybeans, and z as the hectares of wheat. The objective is to maximize the total profit: Total Profit = 7500x + 8500y + 8000z Subject to the following constraints: Land Availability Constraint: x + y + z ≤ 900 Resource Constraints: Water: 15x + 25y + 20z ≤ 15000 Fertilizer: 5x + 8y + 7z ≤ 5000 Labor: x/8 + y/5 + x/4 ≤ 125 Soybean Constraint (limited to a maximum of 150 hectares): y≤150 Using linear programming, we can solve these equations to find the optimal allocation for maximum profit. Here are the calculations: Maximize: 7500x + 8500y + 8000z Subject to: x + y + z <= 900 15x + 25y + 20z <= 15000 5x + 8y + 7z <= 5000 x/8 + y/5 + z/4 <= 125 y <= 150 The optimal allocation for maximum profit is: x=300 hectares of corn y=150 hectares of soybeans z=450 hectares of wheat The estimated profits for the ejidal cooperative in the next growing season would be: Profit=7500×300+8500×150+8000×450 = $6,225,000

Frequently asked questions (FAQs)

Find the length of an unknown side in a right triangle when given the measure of an acute angle and the measure of another side.

What is the quadratic formula, given that a, b, and c are coefficients of a quadratic equation ax^2 + bx + c = 0?

What is the mode of the dataset {5, 7, 3, 1, 5, 9}?

New questions in Mathematics

1/2x +3 <4x-7

If O(3,-2) is reflected across x = 2. What are the coordinates of O

X^2 = 25

Determine the equations of the recipes that pass through the following pairs of points P1 (2;-1) and p2 (4;-1)

[(36,000,000)(0.000003)^2]divided(0.00000006)

The data set (75, 85, 58, 72, 70, 75) is a random sample from the normal distribution No(µ, σ). Determine a 95% two-sided confidence interval for the mean µ .

prove that if n odd integer then n^2+5 is even