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

Let the number of goats raised be x and the number of llamas raised be y

Objective function is to maximize the profit

Max Z = 84x + 126y

Constraints -

2x + 5y <= 400 .... total acres available

100x + 80y <=13200 .... total veterinary care available

x>=0, y>=0

Let us solve using excel solver

Let us initially assume that Goats = 1 and Llamas = 1

The cells in blue color will be optimized to find the maximum profit in the green cell

Run the solver to get -

Hence, the rancher should raise 100 goats and 40 llamas for a maximum profit of $13440