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

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): You can put this solution on YOUR website!
x = number of ounces of product X.
y = number of ounces of product Y.

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

RELATED QUESTIONS
Could you please help me out on this one? Ron ateends a party. He wants to limit his... (answered by stanbon)

Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to... (answered by chen.aavaz)

A dietitian wants a patient to have meal with 66 grams of protein, 94.5 grams of... (answered by Fombitz)

Each serving of Rice Krispies contains 2g of protein and 25g of carbs. Each serving of... (answered by stanbon)

the graph says: nutrition below: serving size-1 bar calories-190 total fat-4.5 g... (answered by math_tutor2020)

One more I am stuck on, I feel like there is something missing. A person who must meet... (answered by ankor@dixie-net.com)

XXX Company produces 2 brands of rabbit food called Food A and Food B, contribution from... (answered by ikleyn)

A dietician is planning a meal of beef, rice and carrots. The meal must contain 96.3g... (answered by Edwin McCravy)

A nutritionist must meet certain requirments and yet keep the weight of a package to a... (answered by stanbon)