A dietitian is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of protein 3 units of carbohydrates, and 2 units of fat, and will contain 40 calories. Each ounce of nuts will supply 2 units of protein,1 unit of carbohydrates, and 4 units of fat, and will contain 50 calories. Every package must provide at least 6 units of protein, at least 15 units of carbohydrates, and no more than 22 units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least number of calories. What is the least number of calories?
Let x be the ounces of fruit and y be the ounces of nuts. What is the objective function that must by minimized?
The objective function that must be minimized is the total number of calories in the snack package.
Since each ounce of fruit contains 40 calories and each ounce of nuts contains 50 calories, the total number of calories in the snack package can be calculated as follows:
Total Calories = (40 * x) + (50 * y)
Therefore, the objective function that must be minimized is:
Minimize: (40 * x) + (50 * y)
the least number of calories. so, you want to minimize
c = 40x + 50y
subject to the given constraints.