Question

Formulate the situation as a linear programming problem by identifying the variables, the objective function, and the constraints. Be sure to state clearly the meaning of each variable. Determine whether a solution exists, and if it does, find it. State your final answer in terms of the original 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, and each llama needs 5 acres of land and requires $80 of veterinary care per year. The rancher can afford no more than $13,200 for veterinary care this year. If the expected profit is $84 for each goat and $126 for each llama, how many of each animal should he raise to obtain the greatest possible profit? The rancher should raise goats and llamas for a maximum profit of $________

Answer 1

Answer:

zero goats and 120 Ilamas to get profit of $15,120

Step-by-step explanation:

Goats: G

Ilamas: l

Explicit constraints:

2G + 5l ≤ 400

100G+ 80l≤ 13,200

Implicit constraints

G≥0

I≥0

P= 84G+ 126l

See attachment for optimal area

substituting coordinats of optimal region in profit equation to get profit

When G= 132, l=0

P=84(132) + 126(0)

P=11,088

When G=0, l=120

P=84(0)+ 126(120)

P = 15120

When G= 100, l=40

P=84(100)+126(40)

P=13440