Question

A rancher raises goats and llamas on his 400-acre ranch. Each goat needs 2 acres of land and requires $100 of veterinary care per year, while each llama needs 5 acres of land and requires $80 of veterinary care per year. If the rancher can afford no more than $13,200 for veterinary care this year, represent this linear programming by the system of linear inequalities. X represent the number of goats the farmer can raise and y represent the number of llamas.

Answer 1

`2x+5y \leq 400\\100x+80y \leq 13,200`

Explanation:

As for the land requirements, total space must not exceed 400 acres, if each goat (x) needs 2 acres, and each llama (y) needs 5 acres, the inequality is:

`2x+5y \leq 400`

As for veterinary care, total expenses must not exceed $13,200, if each goat (x) requires $100, and each llama (y) requires $80, the inequality is:

`100x+80y \leq 13,200`

The system of inequalities that represent this linear programming is:

`2x+5y \leq 400\\100x+80y \leq 13,200`