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.FruitNutsRequirements per packageProteinnothing unit(s) per ouncenothing unit(s) per ounceAt least nothing unit(s) Carbohydratesnothing unit(s) per ouncenothing unit(s) per ounceAt least nothing unit(s)Fatnothing unit(s) per ouncenothing unit(s) per ounceNo more than nothing unit(s)
Accepted Solution
A:
Answer:See explanationStep-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 supplyx units of protein, 2x units of carbohydrates, x units of fatand y ounces of nuts will supplyy 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[tex]\left\{\begin{array}{l}x+y\ge 7\\ 2x+y\ge 11\\x+y\le 10\end{array}\right.[/tex]B. See attached diagram[tex]\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}[/tex]