Question

A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of​ protein, 2 units of​ carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of​ protein, 1 unit of​ carbohydrates, and 1 unit of fat. Every package must provide at least 7 units of​ protein, at least 11 units of​ carbohydrates, and no more than 10 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.
a. Write a system of inequalities to express the conditions of the problem.
b. Graph the feasible region of the system.
a. Fill in the chart.
Fruit
Nuts
Requirements per package
Protein
nothing ​unit(s) per ounce
nothing ​unit(s) per ounce
At least
nothing ​unit(s)
Carbohydrates
nothing ​unit(s) per ounce
nothing ​unit(s) per ounce
At least
nothing ​unit(s)
Fat
nothing ​unit(s) per ounce
nothing ​unit(s) per ounce
No more than
nothing ​unit(s)

Answer 1

Answer:

See explanation

Step-by-step explanation:

Each ounce of fruit will supply

• 1 unit of​ protein,
• 2 units of​ carbohydrates,
• 1 unit of fat.

Each ounce of nuts will supply

• 1 unit of​ protein,
• 1 unit of​ carbohydrates,
• 1 unit of fat.

Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.

Then x ounces of fruit will supply

• x units of​ protein,
• 2x units of​ carbohydrates,
• x units of fat

and y ounces of nuts will supply

• y units of​ protein,
• y units of​ carbohydrates,
• y units of fat.

Every package must provide

• at least 7 units of​ protein, then x+y≥7,
• at least 11 units of​ carbohydrates, then 2x+y≥11,
• and no more than 10 units of fat, then x+y≤10.

A. You get the system of three inequalities

$\left\{\begin{array}{l}x+y\ge 7\\ 2x+y\ge 11\\x+y\le 10\end{array}\right.$

B. See attached diagram

$\begin{array}{cccc}&\text{Protein}&\text{Carbohydrates}&\text{Fat}\\\text{Fruit}&x&2x&x\\\text{Nuts}&y&y&y\\&\text{at least 7}&\text{at least 11}&\text{no more than 10}\end{array}$