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?

Answer 1

To minimize cost and meet minimum requirements, 2 pounds of meat and 0 pounds of cheese are needed, resulting in a minimum cost of $6.80.

Step-by-step explanation:

To minimize the cost and still meet the minimum requirements, we can set up a system of equations.

Let x represent the number of pounds of meat and y represent the number of pounds of cheese.

The total units of carbohydrates can be represented by the equation 2x + 3y = 12, and the total units of protein can be represented by the equation 2x + y = 6.

Solving this system of equations, we find that x = 2 and y = 0.

Thus, 2 pounds of meat and 0 pounds of cheese are needed to meet the minimum requirements while minimizing the cost.

To find the minimum cost, we need to multiply the cost per pound of meat by the number of pounds of meat and the cost per pound of cheese by the number of pounds of cheese.

The cost per pound of meat is $3.40 and the cost per pound of cheese is $3.80.

Substituting the values, we get the minimum cost as 2 pounds * $3.40/pound

= $6.80.