College

We appreciate your visit to Maria desires to increase both her protein consumption and caloric intake She desires to have at least 35 more grams of protein each day and. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Maria desires to increase both her protein consumption and caloric intake. She desires to have at least 35 more grams of protein each day and no more than an additional 200 calories daily. An ounce of milk has 7 grams of protein and 110 calories. An ounce of cheese has 11 grams of protein and 22 calories. Let \( M \) be the number of ounces of milk, and \( C \) be the number of ounces of cheese.

A. Write a system of linear inequalities in two variables that expresses the relationship between the two types of food.

B. Solve the system in part (A). Make sure you label the vertices with exact coordinates.

Answer :

A. a. System of inequalities:

Protein: 7M + 11C ≥ 35

Calories: 110M + 22C ≤ 200

b. Vertices (M, C) satisfying both:

(0, 9.09)

(5, 0)

(2, 5)

B. a. To express the relationship between the two types of food, we can set up the following system of linear inequalities:

Let M be the number of ounces of milk.

Let C be the number of ounces of cheese.

Protein Inequality: Maria wants to consume at least 35 more grams of protein, so the protein inequality can be written as:

7M + 11C ≥ 35

Caloric Inequality: Maria wants to consume no more than an additional 200 calories, so the caloric inequality can be written as:

110M + 22C ≤ 200

b. Now let's solve the system of inequalities. We'll first find the points of intersection by solving for M and C in each inequality separately:

Solving the protein inequality for M:

7M + 11C ≥ 35

M ≥ (35 - 11C) / 7

Solving the caloric inequality for M:

110M + 22C ≤ 200

M ≤ (200 - 22C) / 110

Now, let's plot these inequalities on a graph:

Graph the protein inequality: M ≥ (35 - 11C) / 7

Graph the caloric inequality: M ≤ (200 - 22C) / 110

The points of intersection of these two graphs will give us the possible solutions that satisfy both inequalities. Let's find those points by evaluating the inequalities at the vertices of the feasible region:

Vertices:

(0, 0)

(0, 9.09)

(5, 0)

(2, 5)

Now, plug these values into the original inequalities to see which vertices satisfy both inequalities:

(0, 0):

Protein: 7(0) + 11(0) = 0 < 35 (Not satisfied)

Calories: 110(0) + 22(0) = 0 ≤ 200 (Satisfied)

(0, 9.09):

Protein: 7(0) + 11(9.09) ≈ 100 (Satisfied)

Calories: 110(0) + 22(9.09) ≈ 200 (Satisfied)

(5, 0):

Protein: 7(5) + 11(0) = 35 ≤ 35 (Satisfied)

Calories: 110(5) + 22(0) = 550 > 200 (Not satisfied)

(2, 5):

Protein: 7(2) + 11(5) = 57 > 35 (Satisfied)

Calories: 110(2) + 22(5) = 290 ≤ 200 (Satisfied)

The only vertex that satisfies both inequalities is (0, 9.09). Therefore, Maria can consume 0 ounces of milk and approximately 9.09 ounces of cheese to achieve her desired increase in protein and caloric intake. The coordinates of this vertex are (0, 9.09).

for such more question on Linear Inequalities

https://brainly.com/question/31366329

#SPJ11

Thanks for taking the time to read Maria desires to increase both her protein consumption and caloric intake She desires to have at least 35 more grams of protein each day and. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada