A dietitian is designing a daily diet that is to contain at least 60 units of protein, 40 units of carbs, and 120 units of fat. The diet is to consist of two types of foods. One serving of food A contains 30 units of protein, 10 units of carbs, and 20 units of fat and costs $3. On serving of food B contains 10 units of protein, 10 units of carbs, and 60 units of fat and costs $1.50. Design the diet that provides the daily requirements at the least cost.

To design the diet that meets the daily requirements at the least cost, we need to find the number of servings of each food A and food B that should be included in the diet.

Let's assume we need x servings of food A and y servings of food B.

Each serving of food A contributes 30 units of protein, 10 units of carbs, and 20 units of fat. Therefore, the total units of protein, carbs, and fat from food A can be calculated as:
Protein from food A = 30x
Carbs from food A = 10x
Fat from food A = 20x

Similarly, each serving of food B contributes 10 units of protein, 10 units of carbs, and 60 units of fat. Therefore, the total units of protein, carbs, and fat from food B can be calculated as:
Protein from food B = 10y
Carbs from food B = 10y
Fat from food B = 60y

We need the diet to contain at least 60 units of protein, 40 units of carbs, and 120 units of fat. So we can set up the following inequalities:
30x + 10y ≥ 60 (protein requirement)
10x + 10y ≥ 40 (carbs requirement)
20x + 60y ≥ 120 (fat requirement)

Now let's consider the cost of the diet. Each serving of food A costs $3, and each serving of food B costs $1.50. So the total cost of the diet is given by:
Cost of food A = $3x
Cost of food B = $1.50y
Total cost = $3x + $1.50y

Now, the objective is to minimize the total cost of the diet. This can be achieved by solving the system of inequalities and finding the values of x and y that satisfy the requirements and minimize the cost.

You can use methods like linear programming or graphical methods to solve this system of inequalities and find the values of x and y that minimize the cost.