Question

Suppose that it takes 12 units of carbohydrates and 6 units of protein to satisfy Jacob's minimum weekly requirements.

A particular type of meat contains 2 units of carbohydrates and 2 units of protein per pound. A particular cheese
contains 3 units of carbohydrates and 1 unit of protein per pound. The meat costs $3.40 per pound and the cheese
costs $3.80 per pound. How many pounds of each are needed in order to minimize the cost and still meet the
minimum requirements? What is the minimum cost?
Jacob should buy
pounds of the meat and
pounds of the cheese to yield a minimum cost of $

Answer 1

Suppose that it takes 12 units of carbohydrates and 6 units of protein to satisfy Jacob's minimum weekly requirements. Jacob should buy 2 pounds of meat and 4 pounds of cheese to yield a minimum cost of $22.00.

What is the cost price?

Let m represent the pounds of meat.

Let c represent the pounds of cheese

Set up the following system of equations to represent the requirements:

2m + 3c ≥ 12 (carbohydrate requirement)

2m + c ≥ 6 (protein requirement)

So,

Meat cost: $3.40 per pound

Cheese cost: $3.80 per pound

Find the combination of m and c that satisfies the requirements while minimizing the cost:

Cost function:

Cost = 3.40m + 3.80c

Solve the system of equations and optimize the cost function.

Optimal solution is:

m = 2 (pounds of meat)

c = 4 (pounds of cheese)

Substitute

Cost = 3.40 * 2 + 3.80 * 4

Cost = 6.80 + 15.20

Cost = $22.00

Therefore Jacob should buy 2 pounds of meat and 4 pounds of cheese to yield a minimum cost of $22.00.