A pork producer is considering two types of feed that contain the necessary ingredients for the nutritional requirements for fattening hogs. Brand X contains 2 units of ingredient A per pound and 15 units of ingredient B per pound, Brand Y contains 15 units of ingredient A per pound and 2 units of ingredient B per pound. The nutritional requirements for the hogs are at least 120 units of ingredient A and at least 237 units of ingredient B. If brand X costs 65 cents per pound and brand Y costs 80 cents per pound, how many pounds of each brand should be bought to satisfy the nutritional requirements at minimum cost?

Question

A pork producer is considering two types of feed that contain the necessary ingredients for the nutritional requirements for fattening hogs. Brand X contains 2 units of ingredient A per pound and 15 units of ingredient B per pound, Brand Y contains 15 units of ingredient A per pound and 2 units of ingredient B per pound. The nutritional requirements for the hogs are at least 120 units of ingredient A and at least ​237 units of ingredient B. If brand X costs 65 cents per pound and brand Y costs 80 cents per pound, how many pounds of each brand should be bought to satisfy the nutritional requirements at minimum cost? ​

Quizplus · Accepted Answer

To minimize cost while meeting nutritional requirements, we set up equations based on the given information. Let $x$ be the pounds of Brand X and $y$ be the pounds of Brand Y. The equations based on the nutritional requirements are:- For ingredient A: $2x + 15y \geq 120$- For ingredient B: $15x + 2y \geq 237$To minimize cost: $Cost = 65x + 80y$Solving these equations to meet the requirements at the minimum cost, we find that buying 15 lbs of Brand X and 6 lbs of Brand Y satisfies the nutritional requirements at the lowest cost.

A Pork Producer Is Considering Two Types of Feed That