SOLUTION: You want at least 16g of protein and no more than 50g of carbs at a meal. 1oz of X has 9g of protein and 12g of carbs. 1oz of Y has 4g of protein and 10g of carbs. You want to eat
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-> SOLUTION: You want at least 16g of protein and no more than 50g of carbs at a meal. 1oz of X has 9g of protein and 12g of carbs. 1oz of Y has 4g of protein and 10g of carbs. You want to eat
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Question 1197130: You want at least 16g of protein and no more than 50g of carbs at a meal. 1oz of X has 9g of protein and 12g of carbs. 1oz of Y has 4g of protein and 10g of carbs. You want to eat at least 2oz total food at this meal.
-Identify (name) the 3 constraints and write them as a set of inequalities.
-What combination allows you to eat the minimum ozs of food while also eating exactly 16g of protein? Answer by Theo(13342) (Show Source):
your constraint inequalities are:
9x + 4y >= 16 (ounces of protein constraint)
12x + 10y <= 50 (ounces of carb constraint)
x + y >= 2 (total ounces constraint)
x >= 0
y >= 0
9x + 4y = 16
the first 3 are the inequalities you are looking for.
the next 2 are for graphing purposes to make sure the ounces of either product are greater than or equal to 0.
the last one is to identify where exactly 16 grams of protein are situated on the graph.
your objective function is x + y because you want to find the minimum number of ounces of food that give you exactly 16 ounces of protein.
using the desmos.com calculator, you would graph the opposite of the inequalities and you would evaluate the objective function at the corner points of the feasible region.
the feasible region is the area on the graph that is not shaded.
you can see from the graph that your solution will lie on the line of the equation of 9x + 4y = 16
there are two possibilities.
(x,y) = (0,4) and (1.6,.4)
the objective function is x + y.
that's what you want to minimize.
at (0,4), x + y = 4
at (1.6,.4), x + y = 2
the minimum ounces of food that contain exactly 16 grams of protein are 1.6 ounces of product X and .4 ounces of product Y.
here's your graph.
let me know if you have any questions regarding this.
theo
