Question

A farmer owns 30 acres of land on which he wishes to grow corn and barley. The cost per acre for seed corn is $30, and the cost per acre for barley seed is $20. The farmer can invest a maximum of $600 in seed for the two crops. During the cultivation process, the farmer needs to spray fertilizers and insecticides specific to each crop. This costs $10 per acre for corn and $15 per acre for barley. He can invest only $400 in this process.

Part A: Write the two inequalities that are deciding factors for the number of acres of each crop the farmer will plant, based on the amount of money the farmer will spend on planting and cultivating the two crops.
Part B: Replace the inequality signs in the two inequalities with equal signs. Plot a graph representing the two equations choice of how much of each crop to grow using the Edmentum Graphing Tool and paste it into the box below.
Part C: Should the lines be dotted or solid? Give reasons for both lines. What area should be shaded?

Answer 1

Explanation:

The farmer makes 3.58$

Answer 2

prt a. 30c + 20b ≤

prtb. 5,23

prtc. solid,both equations were less than or equal to some value (non-strict inequality), which means that the boundary value (i.e., the line) is also included in the solution set.

The shaded should be below both lines and above both axes.

Explanation: