Question

a farmer wants to plant two types of crops: corn (x) and wheat (y). each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour of labor. the farmer has a total of 8 hours available. each acre of corn requires 1 bag of fertilizer, and each acre of wheat requires 2 bags. the farmer has a total of 8 bags of fertilizer. the farmer has limits on labor and fertilizer. which inequalities correctly show these limits? (1 point) 2x + y ≤ 8 and x + 2y ≤ 8 2x + y ≥ 8 and x + 2y ≥ 8 x + y ≤ 8 and 2x + 2y ≤ 8 3x + 2y ≤ 8 and x + y ≤ 8

Explanation:

Step1: Analyze labor - hour constraint

Corn (\(x\)) requires 2 hours per acre, wheat (\(y\)) requires 1 hour per acre. Total labor hours available is 8. So, \(2x + y\leq8\).

Step2: Analyze fertilizer - bag constraint

Corn (\(x\)) requires 1 bag per acre, wheat (\(y\)) requires 2 bags per acre. Total fertilizer bags available is 8. So, \(x + 2y\leq8\).

Answer:

\(2x + y\leq8\) and \(x + 2y\leq8\) (first option)