Q. 60 Mixed Nuts Nola鈥檚 Nuts, a stor... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 60 (page 784)

Mixed Nuts Nola鈥檚 Nuts, a store that specializes in selling nuts, has available 90 pounds (lb) of cashews and 120 lb of peanuts. These are to be mixed in 12-ounce (oz) packages as follows: a lower-priced package containing 8 oz of peanuts and 4 oz of cashews and a quality package containing 6 oz of peanuts and 6 oz of cashews.
(a) Use x to denote the number of lower-priced packages and use y to denote the number of quality packages. Write a system of linear inequalities that describes the possible number of each kind of package. (b) Graph the system and label the corner points

Short Answer

Expert verified

$(a) \{\begin{cases} x 鈮� 0 \\ y 鈮� 0 \\ 2 x + 3 y 鈮� 540 \\ 4 x + 3 y 鈮� 720 \end{cases} (b) Corner points are (0, 0), (0, 180) and (135, 0) .$

Step by step solution

Part (a) Step 1. Given information

The goal of the task is to write a system of linear inequalities that describes the possible number of each type of packet x - the number of lower-priced packages; y - the number of quality packages

Part (a) Step 2. Make a table

	Cashews (90)	Peanuts (120)
x	4	8
y	6	6

$12 (90) = 1080 12 (120) = 1440$

Part (a) Step 3. Find the system of linear inequalities

We get a system of inequalities

$4 x + 6 y 鈮� 1080 8 x + 6 y 鈮� 1440 Divide both the equations by 2, 2 x + 3 y 鈮� 540 4 x + 3 y 鈮� 720 The system of linear inequalities is : \{\begin{cases} x 鈮� 0 \\ y 鈮� 0 \\ 2 x + 3 y 鈮� 540 \\ 4 x + 3 y 鈮� 720 \end{cases}$

Part (b) Step 1. Given information

The goal of the problem is to graph the system of linear inequalities.

$\{\begin{cases} x 鈮� 0 \\ y 鈮� 0 \\ 2 x + 3 y 鈮� 540 \\ 4 x + 3 y 鈮� 720 \end{cases}$

Part (b) Step 2. Graph the system

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91影视

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Make a table

Part (a) Step 3. Find the system of linear inequalities

Part (b) Step 1. Given information

Part (b) Step 2. Graph the system

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