Question

A farmer can plant up to eight hectares of land with rice and corn. He can earn Php5000.00 for every hectare he plants with rice and Php 3000.00 for every hectare he plants with corn. His use of a necessary fertilizer is limited by the Credit Cooperative Policy of 10 gallons for his entire 8 hectares. Rice requires 2 gallons of fertilizer for every hectare planted, and corn requires just 1 gallon per hectare.

a. Construct the LP Model
b. Find the farmer's maximum profit.
c. Graph the feasible region.

Answer 1

The LP Model can be constructed to find the farmer's maximum profit by planting rice and corn on up to 8 hectares of land. The feasible region can be graphed to determine the vertex with the highest profit.

Step-by-step explanation:

The LP (Linear Programming) model for the farmer's problem can be constructed as follows:

Let x be the number of hectares of land planted with rice, and y be the number of hectares planted with corn.

Objective function: Maximize profit = 5000x + 3000y

Constraints:

1. x + y ≤ 8 (Total land available is 8 hectares)
2. 2x + y ≤ 10 (Total fertilizer available is 10 gallons)
3. x ≥ 0 (Non-negative condition)
4. y ≥ 0 (Non-negative condition)

To find the maximum profit, you can graph the feasible region and find the vertex with the highest profit.