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=

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)

What is the formula for finding the area of a regular pentagon with a side length of 6 units?

What is the derivative of the function f(x) = ∫(0 to x) t^3 + 2t^2 dt?

Math question: Find the value of y when x=3 in the circle function x^2+y^2=25.

New questions in Mathematics

A circle with a 12-inch diameter is folded in half and then folded in half again. What is the area of the resulting shape?

3(4×-1)-2(×+3)=7(×-1)+2

2/3+5/6×1/2

Find the equation of the line perpendicular to −5𝑥−3𝑦+5=0 passing through the point (0,−2)

The average number of babies born at a hospital is 6 per hour. What is the probability that three babies are born during a particular 1 hour period?

Solve : 15/16 divide 12/8 =x/y

It is known that the content of milk that is actually in a bag distributes normally with an average of 900 grams and variance 25 square grams. Suppose that the cost in pesos of a bag of milk is given by 𝐶(𝑥) = { 3800 𝑠𝑖 𝑥 ≤ 890 4500 𝑠𝑖 𝑥 > 890 Find the expected cost.