Solve the problem.
-A breed of cattle needs at least 10 protein and 8 fat units per day. Feed type I provides 6 protein and 2 fat units at $4 per bag. Feed type II provides 2 protein and 3 fat units at $3 per bag. What mixture of Feed type I and Feed
Type II will fill the dietary needs at minimum cost?
A) 1 bag of Feed type I, 1 bag of Feed type II
B) 1 bag of Feed type I, 2 bags of Feed type II
C) 4 bags of Feed type I, 0 bags of Feed type II
D) 0 bags of Feed type I, 5 bags of Feed type II

Question

Quizplus · Accepted Answer

To meet the minimum dietary needs at the lowest cost, we set up equations based on the protein and fat requirements. Let $x$ be the number of bags of Feed type I and $y$ be the number of bags of Feed type II. For protein, $6x + 2y \geq 10$, and for fat, $2x + 3y \geq 8$. To minimize cost, we minimize $4x + 3y$. Solving these equations, option B (1 bag of Feed type I and 2 bags of Feed type II) meets the dietary requirements (6 protein units from Feed I + 4 protein units from Feed II = 10 protein units, and 2 fat units from Feed I + 6 fat units from Feed II = 8 fat units) at the lowest cost ($4 for Feed I + $6 for Feed II = $10).

Solve the Problem. -A Breed of Cattle Needs at Least 10 Protein and 10