Question

An animal shelter mixes two brands of dry dog food. Brand X costs $25 per bag and contains two units of nutrient A, two units of nutrient B, and two units of nutrient C. Brand Y costs $20 per bag and contains one unit of nutrient A, nine units of nutrient B, and three units of nutrient C. The minimum required amounts of nutrients A, B, and C are 12 units, 36 units, and 24 units, respectively. What is the optimal number of bags of each brand that should be mixed? What is the optimal cost?

Answer 1

Nutrient A constraint: 2x + y ≥ 12

Nutrient B constraint: 2x + 9y ≥ 36

Nutrient C constraint: 2x + 3y ≥ 24

Cost= 25x + 20y

Optimal cost = 25x + 20 y = 25 × 6 + 20 × 2 = 150

Therefore the answer is 150$