Question

2. A farmer is creating a budget for planting soybeans and wheat. Plantingsoybeans costs $200 per acre and planting wheat costs $500 per acre. Hewants to spend no more than $100,000 planting soybeans andwheat.2a. Write an inequality to describe the constraints. Specify what eachvariable represents.*2b. Name one solution to the inequality and explain what it represents inthat situation.*

Answer 1

Planting soybeans cost $200 per acre and planting wheat costs $500 per acre.

He wants to spend no more than $100,000 planting soybeans and wheat.

No more than means that the total cost must be equal to or less than $100,000.

The farmer would be interested in finding the number of acres to plant soybeans and wheat.

Let x represent the number of acres to plant soybeans.

Let y represent the number of acres to plant wheat.

Then we can write the following inequality

`200x+500y\le100,000`

Here 200 and 500 are the cost per acre of planting soybeans and wheat.

x and y are the number of acres to plant soybeans and wheat.

The total cost of planting soybeans and wheat must be equal to or less than $100,000

2b.

Now we need to find out what value of x and y can satisfy the above inequality?

There may be many such values of x and y that may satisfy the inequality.

For example:

Consider x = 200 and y = 100

`\begin{gathered} 200x+500y\le100,000 \\ 200(200)+500(100)\le100,000 \\ 20,000+50,000\le100,000 \\ 70,000\le100,000 \end{gathered}`

As you can see, the inequality is satisfied.

This means that the farmer can plant soybeans on 200 acres and wheat on 100 acres.

This is one of the possible solutions that guarantee that the total cost would be no more than $100,000.